relative extrema calculus

Identify the critical points of the following function:
g(x)=2x³-3x²

• x=-1,1
• x=0,0
• x=0,-1
• x=0,1

The second derivative, y'', gives the ___ of the function.

• slope

• acceleration

• minimum

• concavity

The first derivative, y', gives the ___ of the function.

• slope

• maximum

• velocity

• concavity

Tags

CCSS.HSF.IF.B.4

Find all relative extrema for the function above:

• A

• B

• C

• D

For the function above, find all relative extrema.

• A

• B

• C

• D

Use the second derivative test to determine the relative extrema of

f(x) = x³ – 3x + 5.

Relative MINIMUM when x=___

(Type only the number)

• Relative Maximum at

  x = -1

• Relative Minimum at

  x = 1

• Inflection at

  x = 0

• Relative Maximum at

  x = 1

• Relative Minimum at x = 0

• Relative Maximum at

  x = -1

• Relative Maximum at

  x = 1

• Inflection at

  x = 0

• Relative Minimum at

  x = 1

• Relative Minimum at x = 0