Curve Sketching

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

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

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

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)

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

• 0
• -1
• 2
• 5

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 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'(-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

If f''(x)>0 over the interval (-7,1), then what will be true about f'(x)?

• It's constant
• It's increasing
• It's decreasing
• Cannot be determined

Tags

CCSS.HSF.IF.B.4