First and second derivatives

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.HSF.LE.B.5

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

• increasing
• decreasing
• concave up
• concave down

Let f be the function with derivative given by f'(x) = x² - 2/x.  On which of the following intervals is f decreasing?  (No Calculator)

• (-∞, 0]
• (-1, 0]
• (0, ∛2]
• (∛2, ∞)

Tags

CCSS.HSA.APR.B.3

Given a function, f(x), if f'(x)<0 over a certain interval, then f(x) is ____________ over that interval.

• decreasing
• increasing
• concave up
• concave down

Tags

CCSS.HSF.IF.B.4

For a function g(x), g'(-2)=0 indicates that x=-2 is ________________.

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

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

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

Tags

CCSS.HSA.APR.B.3

What are the intervals of the graph increasing for f(x) = 2x⁴- 4x² + 1

• (-1,0)
• (0,1)
• (-∞,-1) and (1,∞)

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

• 0
• -1
• 2
• 5

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Select the correct derivative of f(x).  

• A.
• B.
• C.
• D.