First Derivative Test

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

• (-∞, -3) ∪ (1, ∞)

• (-3, 1)

• (-5, 0) ∪ (2, ∞)

• (-5, ∞)

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

The slope of a function is described by its ____________.

• first derivative

• second derivative

• third derivative

• expression

If  $f'\left(a\right)=0$  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

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

What is the relative minimum x value of 

 $y=x^3+6x^2$  

• -4

• 0

• 12

• 4

Tags

CCSS.HSA.APR.B.3