The population of a town x years after 2000 is modeled by P(x). What is the best interpretation of P'(10) = 50.

In 2010, the population was increasing 50 people per year.

In 2010, the population was 50 people.

It took 10 years for the population to increase by 50 people.

The average change in population over the 10 years was 50 people per year.

Set up the derivative of y=(3x 4 - 7)*(5x 2 + 1)

(3x 4 - 7)*(10x) + (12x 3 )*(5x 2 + 1)

(3x 4 - 7)*(10x) - (12x 3 )*(5x 2 + 1)

(3x 4 - 7)/(10x) + (12x 3 )/(5x 2 + 1)

Identify the interval(s) of decrease.

( − 3 , − 1 ) , ( 2 , 4 ) \left(-3,\ -1\right),\ \left(2,\ 4\right) ( − 3 , − 1 ) , ( 2 , 4 )

( − ∞ , − 3 ) , ( − 1 , 2 ) , ( 4 , ∞ ) \left(-\infty,\ -3\right),\ \left(-1,\ 2\right),\ \left(4,\ \infty\right) ( − ∞ , − 3 ) , ( − 1 , 2 ) , ( 4 , ∞ )

( − ∞ , − 3 ) , ( ( 4 , ∞ ) ) \left(-\infty,\ -3\right),\ \left(\left(4,\ \infty\right)\right) ( − ∞ , − 3 ) , ( ( 4 , ∞ ) )

( 2 , − 3 ) , ( 1 , − 1 ) \left(2,\ -3\right),\ \left(1,\ -1\right) ( 2 , − 3 ) , ( 1 , − 1 )

Identify the interval(s) of increase.

( − ∞ , − 3 ) , ( − 1 , 2 ) , ( 4 , ∞ ) \left(-\infty,\ -3\right),\ \left(-1,\ 2\right),\ \left(4,\ \infty\right) ( − ∞ , − 3 ) , ( − 1 , 2 ) , ( 4 , ∞ )

( − ∞ , − 3 ) , ( ( 4 , ∞ ) ) \left(-\infty,\ -3\right),\ \left(\left(4,\ \infty\right)\right) ( − ∞ , − 3 ) , ( ( 4 , ∞ ) )

( 2 , − 3 ) , ( 1 , − 1 ) \left(2,\ -3\right),\ \left(1,\ -1\right) ( 2 , − 3 ) , ( 1 , − 1 )

( − 3 , − 1 ) , ( 2 , 4 ) \left(-3,\ -1\right),\ \left(2,\ 4\right) ( − 3 , − 1 ) , ( 2 , 4 )

Derivatives Practice

Authored by Chuck Rathfelder

Mathematics

11th - 12th Grade

CCSS covered

Used 98+ times

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the derivative of f(x) = 5x² + 7x - 3.

2x + 7

10x + 7

10x + 4

2x + 4

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

4x⁹ + 6x⁷

(2/5)x⁹ + (3/4)x⁷

20x⁹ + 24x⁷

x⁹ + x⁷

Differentiate y = -19

-19

Not differentiable

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Differetiate y = -19x

-19

Not differentiable

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

(1/2)x^-7

(1/2)x^-9

-32x^-9

-32x^-7

Find the derivative:
y = (4x - 5)(2x + 3)

16x

16x + 2

What is the derivative of sin(x)?

sin(x)

cos(x)

-sin(x)

-cos(x)

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Derivatives Practice