Analyzing Graphs

Which one of the following statements is always true?

• When a graph is increasing, its derivative is negative.

• When a graph is decreasing, so is its derivative.

• When a graph is decreasing, its derivative is negative.

• When a graph is increasing, so is its derivative.

Tags

CCSS.HSF.IF.B.4

f(x) is a polynomial function. Which one of the following statements is FALSE?

• f(x) has a derivative of zero when the graph of f has a relative min or max.

• If the derivative of f(x) changes from positive to negative at some point, then the graph of f has a relative minimum at that point.

• If the derivative of f(x) is always positive, then the graph of f has no relative extrema.

• If the graph of f is always increasing, then the derivative of f(x) is never negative.

7.

• (A)

• (B)

• (C)

• (D)

Select the correct derivative of f(x).

• A.

• B.

• C.

• D.

Tags

CCSS.HSF-IF.C.7A

When f'(x) changes from positive to negative, f(x) has ...

• a maximum.
• a minimum.
• no extrema.

f' is given, which could be f?

• A
• B
• C

f'(x) is pictured. Which x values does f(x) has a relative max?

• x=-5 and -1

• x=-3

• x=-1

• x=-5

• local maximum

• local minimum

• zero

Which one of the following statements is always true?

• When f(x) is increasing, its derivative is increasing.

• When f(x) is decreasing, f''(x) is negative.

• When f'(x) is decreasing, f(x) is concave down.

• When f'(x) is increasing, f(x) is positive

Tags

CCSS.HSF.IF.B.4

According to the graph, at the point x=-2, is f(x) increasing or decreasing and why?

• At x=-2 f(x) is increasing because f'(x) has a positive slope.

• At x=-2 f(x) is decreasing because f'(x) has a positive slope.

• At x=-2 f(x) is decreasing because f'(x) lies below the x-axis.

• At x=-2 f(x) is decreasing because f'(x) has a negative slope

Tags

CCSS.HSF.IF.B.4