Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 6 sin ⁡ x − 3 2 x f\left(x\right)=6\sin x-3\sqrt{2}x f ( x ) = 6 sin x − 3 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x . Select ALL that apply

x = 7 π 4 x=\frac{7\pi}{4} x = 4 7 π

x = π 4 x=\frac{\pi}{4} x = 4 π

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = 5 π 4 x=\frac{5\pi}{4} x = 4 5 π

Given 0 ≤ x ≤ 2 π 0\le x\le2\pi 0 ≤ x ≤ 2 π , Find ALL the critical numbers in f ( x ) = sin ⁡ x f\left(x\right)=\sin x f ( x ) = sin x

x = 3 π 2 x=\frac{3\pi}{2} x = 2 3 π

x = π 2 x=\frac{\pi}{2} x = 2 π

Given 0 ≤ x ≤ 2 π 0\le x\le2\pi 0 ≤ x ≤ 2 π , Find ALL the critical numbers in f ( x ) = cos ⁡ x f\left(x\right)=\cos x f ( x ) = cos x . Select ALL that apply.

x = 3 π 2 x=\frac{3\pi}{2} x = 2 3 π

x = π 2 x=\frac{\pi}{2} x = 2 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 10 sin ⁡ x + 5 2 x f\left(x\right)=10\sin x+5\sqrt{2}x f ( x ) = 1 0 sin x + 5 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x . Select ALL that apply

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = 5 π 4 x=\frac{5\pi}{4} x = 4 5 π

x = 7 π 4 x=\frac{7\pi}{4} x = 4 7 π

x = π 4 x=\frac{\pi}{4} x = 4 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 8 cos ⁡ x − 4 2 x f\left(x\right)=8\cos x-4\sqrt{2}x f ( x ) = 8 cos x − 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x . Select ALL that apply

x = 5 π 4 x=\frac{5\pi}{4} x = 4 5 π

x = 7 π 4 x=\frac{7\pi}{4} x = 4 7 π

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = π 4 x=\frac{\pi}{4} x = 4 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 18 cos ⁡ x + 9 2 x f\left(x\right)=18\cos x+9\sqrt{2}x f ( x ) = 1 8 cos x + 9 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x . Select ALL that apply

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = π 4 x=\frac{\pi}{4} x = 4 π

x = 7 π 4 x=\frac{7\pi}{4} x = 4 7 π

x = 5 π 4 x=\frac{5\pi}{4} x = 4 5 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 4 sin ⁡ x − 2 3 x f\left(x\right)=4\sin x-2\sqrt{3}x f ( x ) = 4 sin x − 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x . Select ALL that apply

x = π 6 x=\frac{\pi}{6} x = 6 π

x = 11 π 6 x=\frac{11\pi}{6} x = 6 1 1 π

x = 5 π 6 x=\frac{5\pi}{6} x = 6 5 π

x = 7 π 6 x=\frac{7\pi}{6} x = 6 7 π

x = 5 π 3 x=\frac{5\pi}{3} x = 3 5 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = − 6 cos ⁡ x + 3 3 x f\left(x\right)=-6\cos x+3\sqrt{3}x f ( x ) = − 6 cos x + 3 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> x . Select ALL that apply

x = 5 π 3 x=\frac{5\pi}{3} x = 3 5 π

x = 4 π 3 x=\frac{4\pi}{3} x = 3 4 π

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = 2 π 3 x=\frac{2\pi}{3} x = 3 2 π

x = π 3 x=\frac{\pi}{3} x = 3 π

Given 0 ≤ x ≤ 2 π 0\le x\le2\pi 0 ≤ x ≤ 2 π , Find ALL the critical numbers in f ( x ) = 2 sin ⁡ x − 2 x f\left(x\right)=2\sin x-2x f ( x ) = 2 sin x − 2 x . Select ALL that apply.

x = 3 π 2 x=\frac{3\pi}{2} x = 2 3 π

x = π 2 x=\frac{\pi}{2} x = 2 π

Given 0 ≤ x ≤ 2 π 0\le x\le2\pi 0 ≤ x ≤ 2 π , Find ALL the critical numbers in f ( x ) = 5 cos ⁡ x − 5 x f\left(x\right)=5\cos x-5x f ( x ) = 5 cos x − 5 x . Select ALL that apply.

x = 3 π 2 x=\frac{3\pi}{2} x = 2 3 π

x = π 2 x=\frac{\pi}{2} x = 2 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 6 sin ⁡ x − 3 x f\left(x\right)=6\sin x-3x f ( x ) = 6 sin x − 3 x . Select ALL that apply

x = π 3 x=\frac{\pi}{3} x = 3 π

x = 5 π 3 x=\frac{5\pi}{3} x = 3 5 π

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = 2 π 3 x=\frac{2\pi}{3} x = 3 2 π

x = 4 π 3 x=\frac{4\pi}{3} x = 3 4 π

Given ( 0 ≤ x ≤ 2 π ) \left(0\le x\le2\pi\right) ( 0 ≤ x ≤ 2 π ) Find ALL the critical numbers in f ( x ) = 14 cos ⁡ x + 7 x f\left(x\right)=14\cos x+7x f ( x ) = 1 4 cos x + 7 x . Select ALL that apply

x = π 6 x=\frac{\pi}{6} x = 6 π

x = 5 π 6 x=\frac{5\pi}{6} x = 6 5 π

x = 7 π 6 x=\frac{7\pi}{6} x = 6 7 π

x = 11 π 6 x=\frac{11\pi}{6} x = 6 1 1 π

x = 5 π 3 x=\frac{5\pi}{3} x = 3 5 π

Given 0 ≤ x ≤ 2 π 0\le x\le2\pi 0 ≤ x ≤ 2 π , Find ALL the critical numbers in f ( x ) = 3 sin ⁡ x + 3 cos ⁡ x f\left(x\right)=3\sin x+3\cos x f ( x ) = 3 sin x + 3 cos x . Select ALL that apply.

x = π 4 x=\frac{\pi}{4} x = 4 π

x = 5 π 4 x=\frac{5\pi}{4} x = 4 5 π

x = 3 π 4 x=\frac{3\pi}{4} x = 4 3 π

x = 7 π 4 x=\frac{7\pi}{4} x = 4 7 π

Calculus Critical Numbers, Relative and Absolute Extrema

Authored by Adeyemi Aderinto

Mathematics

10th Grade - University

CCSS covered

Used 133+ times

Calculus Critical Numbers, Relative and Absolute Extrema

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26 questions

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MULTIPLE SELECT QUESTION

15 mins • 1 pt

Use the diagram to classify relative and absolute extrema.
Select ALL that apply.

A is an absolute minimum

B is a relative maximum

C is an absolute minimum

D is an relative minimum

E is an relative minimum

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Use the diagram to classify relative and absolute extrema.
Select ALL that apply.

(0,0) is an absolute minimum

(1,-14) is an absolute minimum

(4, 40) is an absolute maximum

(6, 10) is an relative minimum

(7, 65) is an absolute maximum

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the critical number of f(x) = 4x² – 8x + 1

x = 2

x = 0

x = 8

x = 1

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Find all the critical numbers of
f(x) = x³ – 6x² + 10.
Select ALL that apply

x = 4

x = 6

x = -2

x = 0

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Find all the critical numbers of
f(x) = 2x³ – 6x² + 12
Select ALL that apply.

x= 4

x= 0

x= -2

x= 2

MULTIPLE SELECT QUESTION

15 mins • 1 pt

$f\left(x\right)=\frac{2}{3}x^3-18x^2-80x+17$
Find all the critical numbers of f(x) above
Select ALL that apply.

x= -10

x= 20

x= -8

x= -2

MULTIPLE SELECT QUESTION

15 mins • 1 pt

$f\left(x\right)=\frac{1}{3}x^3+3x^2+8x-5$
Find the critical numbers of f(x). Select ALL that apply

x=2

x=0

x= -4

x= -2

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Find all the critical numbers of f(x).
$f\left(x\right)=\frac{1}{4}x^4-\frac{5}{3}x^3-7x^2+13$
Select ALL that apply.

x= 7

x= 5

x= 0

x = -2

x = 14

10.

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Given $\left(0\le x\le2\pi\right)$ Find ALL the critical numbers in $f\left(x\right)=6\sin x-3\sqrt{2}x$ . Select ALL that apply

$x=\frac{7\pi}{4}$

$x=\frac{3\pi}{4}$

$x=\frac{\pi}{4}$

$x=\frac{5\pi}{4}$

$x=\pi$

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Calculus Critical Numbers, Relative and Absolute Extrema

Use the diagram to classify relative and absolute extrema. Select ALL that apply.

Use the diagram to classify relative and absolute extrema.Select ALL that apply.

Find the critical number of f(x) = 4x2 – 8x + 1

Find all the critical numbers of f(x) = x3 – 6x2 + 10. Select ALL that apply

Find all the critical numbers off(x) = 2x3 – 6x2 + 12Select ALL that apply.

f(x)=23x3−18x2−80x+17f\left(x\right)=\frac{2}{3}x^3-18x^2-80x+17f(x)=32​x3−18x2−80x+17 Find all the critical numbers of f(x) aboveSelect ALL that apply.

f(x)=13x3+3x2+8x−5f\left(x\right)=\frac{1}{3}x^3+3x^2+8x-5f(x)=31​x3+3x2+8x−5 Find the critical numbers of f(x). Select ALL that apply

Find all the critical numbers of f(x) = 6x4 – 16x3 – 180x2 + 456.Select ALL that apply

Find all the critical numbers of f(x). f(x)=14x4−53x3−7x2+13f\left(x\right)=\frac{1}{4}x^4-\frac{5}{3}x^3-7x^2+13f(x)=41​x4−35​x3−7x2+13 Select ALL that apply.

Given (0≤x≤2π)\left(0\le x\le2\pi\right)(0≤x≤2π) Find ALL the critical numbers in f(x)=6sin⁡x−32xf\left(x\right)=6\sin x-3\sqrt{2}xf(x)=6sinx−32​x . Select ALL that apply

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Discover more resources for Mathematics

Use the diagram to classify relative and absolute extrema.
Select ALL that apply.

Use the diagram to classify relative and absolute extrema.
Select ALL that apply.

Find the critical number of f(x) = 4x² – 8x + 1

Find all the critical numbers of
f(x) = x³ – 6x² + 10.
Select ALL that apply

Find all the critical numbers of
f(x) = 2x³ – 6x² + 12
Select ALL that apply.

$f\left(x\right)=\frac{2}{3}x^3-18x^2-80x+17$
Find all the critical numbers of f(x) above
Select ALL that apply.

$f\left(x\right)=\frac{1}{3}x^3+3x^2+8x-5$
Find the critical numbers of f(x). Select ALL that apply

Find all the critical numbers of
f(x) = 6x⁴ – 16x³ – 180x² + 456.
Select ALL that apply

Find all the critical numbers of f(x).
$f\left(x\right)=\frac{1}{4}x^4-\frac{5}{3}x^3-7x^2+13$
Select ALL that apply.

Given $\left(0\le x\le2\pi\right)$ Find ALL the critical numbers in $f\left(x\right)=6\sin x-3\sqrt{2}x$ . Select ALL that apply