Extrema & Concavity

Identify the interval from the derivative graph where the function is concave up.

• (-1,1) & (3,4)
• (-3,-2)
• (-2,-1)
• (-3,-1) & (1,3)

Identify the interval from the derivative graph where the function is concave down

• (-1,1) & (3,4)
• (-2,4)
• (-3,-1) & (1,3)
• (-2,1) & (1,4)

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

• a maximum.

• a minimum.

• no extrema.

• an inflection point.

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

• a maximum.

• a minimum.

• no extrema.

• an inflection point.

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

Over what intervals is f(x) decreasing?

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

Find the critical points of f(x) = 2x⁴- 4x² + 1

• x= 0
• x = -1, 1
• x = -1, 0, 1
• no critical points

What will be true at an inflection point?  (select the best answer)

• f(x)=0
• f'(x)=0
• f''(x)=0
• The function is undefined

For a function g(x), g''(3)=-8 indicates that g(x) is ____________ at x=3.

• increasing
• decreasing
• concave up
• concave down

Tags

CCSS.HSF-BF.B.4A

For a function f(x), f''(4)=0 indicates that x=4 is _____________.

• an inflection point
• a critical point
• a relative maximum
• a relative minimum