Curve sketching review

Front

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

Back

concave down

Front

If a function's FIRST derivative is negative at a certain point, what does that tell you?

Back

The function is decreasing at that point.

Front

List all of the x-locations of the minimum points of the function whose derivative is graphed.

Back

{-1}

Front

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

Back

increasing

Front

Which graph is the derivative of the top graph?

Back

A

Front

What does it mean if the second derivative of a function is positive at a point?

Back

The function is concave up at that point.

Front

What does it mean if the first derivative of a function is zero at a point?

Back

The function has a critical point at that location.

Front

If f'(x) changes from positive to negative at x=c, what can be concluded about f(x)?

Back

f(x) has a local maximum at x=c.

Front

If f'(x) changes from negative to positive at x=c, what can be concluded about f(x)?

Back

f(x) has a local minimum at x=c.

Front

What is the relationship between the first derivative and the increasing/decreasing behavior of a function?

Back

If f'(x) > 0, f(x) is increasing; if f'(x) < 0, f(x) is decreasing.