5-3 & 5-4 The First Derivative Test

Presentation

•

Mathematics

•

11th Grade

•

Medium

•

CCSS

8.EE.B.5

Standards-aligned

Jessica Stewart

Used 13+ times

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3 Slides • 10 Questions

5-3 & 5-4 The First Derivative Test

Guided Notes

Multiple Choice

The slope of a function is described by its ____________.

first derivative

second derivative

third derivative

expression

Multiple Choice

If a function's FIRST derivative is negative at a certain point, what does that tell you?

The function is increasing at that point

The function is decreasing at that point

The concavity of the function is up at that point

The concavity of the function is down at that point

Multiple Choice

Over what interval(s) is f(x) decreasing?

(-3, 1)

(-∞, -5) ∪ (0, 2)

(-∞, -3) ∪ (1, ∞)

(-5, 0) ∪ (2, ∞)

Multiple Choice

Over what interval(s) is f(x) increasing?

(-∞, -3) ∪ (1, ∞)

(-3, 1)

(-5, 0) ∪ (2, ∞)

(-5, ∞)

Multiple Choice

Over what intervals is f(x) decreasing?

(-∞, -1) ∪ (1, ∞)

(-∞, -√3) ∪ (0, √3)

(-1, 1)

(-√3, 0) ∪ (√3, ∞)

Multiple Choice

If $f'\left(x\right)=0$ and $f'\left(a\right)=0$ changes from negative to positive at $f'\left(x\right)$ , then $x=a$ has

a relative maximum at x=a

a relative minimum at x=a

no relative extrema at x=a

a vertical tangent line at x=a

Multiple Choice

If $f'\left(x\right)$ and $f'\left(x\right)$ changes from positive to negative at $x=a$ , then $f\left(x\right)$ has

A relative maximum at x=a

A relative minimum at x=a

No relative extrema at x=a

A vertical tangent line at x=a

Multiple Choice

The function $f\left(x\right)=-x^3+3x^2-5$ has a relative maximum value of _____________ at x=_____________.

0; -5

-5; 0

2; -1

-1; 2

Multiple Choice

If $\ f'\left(a\right)=0$ , then you are guaranteed a relative extreme value at x=a.

True

False

Multiple Choice

Which of the following could be the graph of f ' , the derivative of f ?

5-3 & 5-4 The First Derivative Test

Guided Notes

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