Connecting F to F Prime and F Double Prime

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.

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.

Identify the critical points of the following function:
g(x)=2x³-3x²

• x=-1,1
• x=0,0
• x=0,-1
• x=0,1

f''(x) is pictured. Which x values are inflection points of f(x)?

• x=-5 and -1
• x=-3
• x=4
• no inflection points

For a function g(x), g'(-2)=0 indicates that x=-2 is ________________.

• an inflection point
• a critical point
• a relative maximum
• a relative minimum

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

• increasing
• decreasing
• concave up
• concave down

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

Select the correct derivative of f(x).

• A.

• B.

• C.

• D.

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

• increasing
• decreasing
• concave up
• concave down

f(x) is pictured. Inflection points are most likely at which x values?

• x=0 and 1.5
• x=2 and 2.5
• x=2.25
• x=1