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Mathematics

11th Grade - University

CCSS covered

First Derivative Test
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7 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Media Image

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

(-∞, -3) ∪ (1, ∞)
(-3, 1)
(-5, 0) ∪ (2, ∞)
(-5, ∞)

2.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

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

3.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

The slope of a function is described by its ____________.

first derivative
second derivative
third derivative
expression

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The function  f(x)=−x3+3x2−5f\left(x\right)=-x^3+3x^2-5  has a relative maximum value of _____________ at x=_____________.

0; -5

-5; 0

2; -1

-1; 2

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

6.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What is the maximum value of f(x) = x3 - 3x2 - 1 on the interval [-3, 2]?

0
-1
2
5

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the relative minimum x value of 

 y=x3+6x2y=x^3+6x^2  

-4

0

12

4

Tags

CCSS.HSA.APR.B.3

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