First Derivative graphs

Multiple Choice

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.

Multiple Choice

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.

Multiple Choice

What is the average rate of change of the function below over the indicated interval?
f(x) = x² + 5x + 5,  [-2,6]

• 9
• 1
• 72
• 0

Multiple Choice

7.

• (A)

• (B)

• (C)

• (D)

Multiple Choice

Select the correct derivative of f(x).

• A.

• B.

• C.

• D.

Multiple Choice

If given f'(x) how would you find the intervals which the graph f(x) has a positive slope?

• f'(x) < 0 (negative)
• f'(x) > 0 (positive)
• f'(x) is increasing
• Can't be determined

Multiple Choice

When f'(x) changes from positive to negative, there is(are) ...

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

Multiple Choice

f' is given, which could be f?

• A
• B
• C

Multiple Choice

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

• x=-5 and -1

• x=-3

• x=-1

• x=-5

Multiple Choice

In the following picture, what does the

$$+$$  
mean about the graph of  $$f\left(x\right)$$  

• $$f\left(x\right)$$  is increasing

• $$f\left(x\right)$$  is decreasing

• $$f\left(x\right)$$  is positive

• $$f\left(x\right)$$  is negative

Multiple Choice

Consider the  $$f'\left(x\right)$$  sign chart.  What can you conclude about the point  $$x=2$$  on  $$f\left(x\right)$$  ?

• local maximum

• local minimum

• stationary point/platuae point

Multiple Choice

When  $$f'\left(x\right)$$  changes from positive to negative, this is called a 

• local maximum

• local minimum

• stationary point

Multiple Choice

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.

Multiple Choice

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

• x=-5 and -1

• x=-3

• x=-1

• x=-5

Multiple Choice

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

• x=-5 and -1

• x=-3

• x=-1

• x=-5

Multiple Choice

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 the graph has a positive slope.

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

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

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

Multiple Choice

Which graph represents the derivative of this graph?

Multiple Choice

• A

• B

• C

• D