First Derivative Test Review

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

• 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

• 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

Where can critical values occur? (check all that apply)

• Enpoints

• x-intercepts

• when f'(x)=0

• when f'(x) is undefined

In order for the Extreme Value Theorem to hold, what must be true? (check all that apply)

• Closed interval

• Open interval

• Continuous function

• Discontinuous Function

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

• (-∞, -3) ∪ (1, ∞)
• (-3, 1)
• (-5, 0) ∪ (2, ∞)
• (-5, ∞)

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

• increasing
• decreasing
• concave up
• concave down

Tags

CCSS.HSA.APR.A.1

Tags

CCSS.HSA.APR.A.1