MCV U4 - Critical points

When f'(x) changes from negative to positive, there is(are) ...

• a maximum.
• a minimum.
• no extrema.

Use the sign chart for f'(x).
There is(are) ...

• a local maximum at x = -2.
• a local maximum at x = 4.
• local maxima at x = -2 and x = 4.
• no extrema.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Given the following graph of f', the derivative of f. For what x-value does f have a relative minimum?

• x=-1 and x=4
• x=-3
• x=1
• x=3

Tags

CCSS.HSF.IF.B.4

When f'(x) changes from positive to negative, there is(are) ...

• a maximum.
• a minimum.
• no extrema.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

 If (a,b) is a local minimum, then what will be true about f'(a)?

• It's positive
• It's negative
• It's zero
• Cannot be determined

Find the relative minimum values for f(x)=3x⁴-2x³-9x²

• -1

• 0

• 1.5

• -1 and 1.5

Tags

CCSS.HSF.IF.B.4

CCSS.HSA.APR.B.3

CCSS.HSF.IF.C.7

The acceleration function is the first derivative of...

• position
• velocity
• calculus
• particle motion

If f'(x) = 0 what does that imply about the x value?

• It is a critical point, it is a possible max, min, or point of inflection.

• That the limit does not exist.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

• x=-1,1
• x=0,0
• x=0,-1
• x=0,1

Tags

CCSS.HSA.APR.B.3

Over what intervals is f(x) decreasing?

• (-∞, -1) ∪ (1, ∞)
• (-∞, -√3) ∪ (0, √3)
• (-1, 1)
• (-√3, 0) ∪ (√3, ∞)

Tags

CCSS.HSA.APR.B.3