Curve Sketching

If f '(3) = 0 and f"(3) < 0, then which of the following must be true?

• There is a local max at x=3
• There is a local min at x = 3
• There is an inflection point at x = 3
• There is an x-intercept at x = 3

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

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

• increasing
• decreasing
• concave up
• concave down

If $x=3$  is a critical point of  $f\left(x\right),$ and  $f''\left(x\right)\ =\ e^{-x}\left(x^2-2x-4\right)$ then $x=3$   is a 

• local maximum

• local minimum

• neither 

Where does the global maximum of $f\left(x\right)\ =\ e^{-x^2}$  occur on  $\left[-1,2\right]$ ? 

•  $x=-1$  

•  $x=0$  

•  $x=1$  

•  $x=2$  

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

Find the intervals of concavity for

f(x) = x² + 2x + 1.

• concave up: (-∞,∞)

• concave down: (-∞,∞)

• concave up: (2, ∞)

  concave down: (-∞,2)

• concave up: (-∞,2)

  concave down: (2, ∞)

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

• -1

• 0

• 1.5

• -1 and 1.5

Tags

CCSS.HSA.APR.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Over what intervals is f(x) decreasing?

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

Tags

CCSS.HSA.APR.B.3

Find the point(s) of inflection for f(x) = 2(x)^1/5 + 3

• None

• x = 0

• x = 0, 2

• x = -2, 0, 2

Tags

CCSS.HSF-IF.C.7D