Final Review: Curve Sketching

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

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

• increasing
• decreasing
• concave up
• concave down

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

• increasing
• decreasing
• concave up
• concave down

If a function's FIRST derivative is negative at a certain point, what does that tell you?

• The function is increasing at that point
• The function is decreasing at that point
• The concavity of the function is up at that point
• The concavity of the function is down at that point

Tags

CCSS.HSF.IF.B.4

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

• (-1,0)

• (0,1)

• (-∞,-1) and (0,1)

• (1,∞) and (-1,0)

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

Where is the point of infection for the function y = x³ + 6x²?

• 0

• -4

• -2

• 4

Tags

CCSS.HSF-IF.C.7C

On what interval(s) is the function y=x³ + 6x²

concave down?

• (-∞,-4)

• (-∞,-2)

• (-2,∞)

• (0,∞)

Over what intervals is f(x) decreasing?

• (-∞, -1) ∪ (1, ∞)

• (1, ∞)

• (-1, 1)

• (-√3, 0) ∪ (√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