Graphs & Derivatives

Front

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.

Back

When a graph is decreasing, its derivative is negative.

Front

Which statement about the polynomial function f(x) 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.

Back

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.

Front

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

Back

x=-5 and -1

Front

For a function g(x), g'(-2)=0 indicates that x=-2 is ________________. Options: an inflection point, a critical point, a relative maximum, a relative minimum

Back

a critical point

Front

How to find intervals where f(x) has a positive slope given f'(x)?

Back

f'(x) > 0 (positive)

Front

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

Back

a maximum.

Front

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

Back

It's increasing

Front

f' is given, which could be f? Options: A, B, C

Back

C

Front

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

Back

It's decreasing

Front

If f''(x)<0 over the interval (0,3), then what will be true about f(x)?

Back

f(x) is concave down