First Derivative Test

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

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

• True

• False

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

Find all relative extrema for the function above:

• A

• B

• C

• D

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

For the function above, find all relative extrema.

• A

• B

• C

• D

Tags

CCSS.HSA.APR.B.3

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