Quiz about Applications of Derivatives

Question 1

What is the lowest point on a function called?

Accepted Answer

absolute minimum

Answer

relative maximum

Answer

relative minimum

Answer

absolute maximum

Question 2

What is the highest point on a function called?

Accepted Answer

absolute maximum

Answer

relative minimum

Answer

relative maximum

Answer

absolute minimum

Question 3

What is the "top of a hill" on a function (even if it is a cusp) called?

Accepted Answer

relative maximum

Answer

relative minimum

Answer

absolute minimum

Answer

absolute maximum

Question 4

What is the "bottom of a valley" on a function (even if it is a cusp) called?

Accepted Answer

relative minumum

Answer

relative maximum

Answer

absolute minimum

Answer

absolute maximum

Question 5

Critical numbers occur where the first derivative is what? (Check all that apply).

Accepted Answer

undefined

Accepted Answer

zero

Answer

endpoint

Answer

maximum

Question 6

Absolute extrema can occur at which of the following? (Check all that apply.)

Accepted Answer

endpoints

Accepted Answer

relative maximum

Accepted Answer

relative minimum

Accepted Answer

critical numbers

Question 7

A function is increasing if its first derivative is what?

Accepted Answer

positive

Answer

undefined

Answer

negative

Answer

zero

Question 8

A function is decreasing if its first derivative is what?

Accepted Answer

negative

Answer

positive

Answer

zero

Answer

undefined

Question 9

What values separate intervals of increasing and decreasing?

Accepted Answer

critical numbers

Answer

possible points of inflection

Question 10

If a function switches from increasing to decreasing, what occurs between?

Accepted Answer

relative maximum

Answer

absolute maximum

Answer

absolute minimum

Answer

relative minimum

Question 11

If a function switches from decreasing to increasing, what occurs between?

Accepted Answer

relative minimum

Answer

absolute maximum

Answer

absolute minimum

Answer

relative maximum

Question 12

What are two ways to identify relative extrema of a function?

Accepted Answer

First Derivative Test

Accepted Answer

Second Derivative Test

Answer

Mean Value Theorem

Question 13

A function is what if its second derivative is negative?

Accepted Answer

concave down

Answer

increasing

Answer

decreasing

Answer

concave up

Question 14

A function is what if its second derivative is positive?

Accepted Answer

concave up

Answer

increasing

Answer

decreasing

Answer

concave down

Question 15

If a function is concave down at a critical number, what must occur at that critical number?

Accepted Answer

relative maximum

Answer

absolute maximum

Answer

absolute minimum

Answer

relative minimum

Question 16

If a function is concave up at a critical number, what must occur at that critical number?

Accepted Answer

relative minimum

Answer

absolute maximum

Answer

absolute minimum

Answer

relative maximum

Question 17

What are identified by finding where the second derivative equals zero or is undefined?

Accepted Answer

possible points of inflection

Answer

relative extrema

Answer

points of inflection

Answer

absolute extrema

Question 18

To be called a point of inflection of a function, what must what happen?

Accepted Answer

concavity must change

Answer

function must be decreasing

Answer

first derivative must equal zero or be undefined

Answer

function must be increasing

Question 19

Identify ALL conditions of Rolle's Theorem.

Accepted Answer

f must be continuous on [a, b]

Accepted Answer

$f\left(a\right)=f\left(b\right)$

Accepted Answer

f must be differentiable on (a, b)

Answer

derivative must equal the slope of secant connecting the endpoints

Question 20

Identify ALL conditions of the Mean Value Theorem.

Accepted Answer

f must be continuous on [a, b]

Accepted Answer

f must be differentiable on (a, b)

Answer

$f\left(a\right)=f\left(b\right)$

Answer

derivative must equal the slope of secant connecting the endpoints

Applications of Derivatives

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