Derivative Behaviors (f, f', f")

Front

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

Back

a critical point

Front

If f''(x)>0, then what will be true about f'(x) over that same interval?

Back

f '(x) is increasing

Front

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

Back

increasing

Front

What will be true at an inflection point? (select the best answer)

Back

f''(x)=0 and there is a sign change

Front

The function shown is the graph of f '(x), the derivative of f(x). The domain is [-3,5]. On which interval is the graph of f(x) concave upward?

Back

(-1,1) & (3,5]

Front

What does it mean if f'(x) = 0 at a point?

Back

It indicates a potential local maximum or minimum.

Front

If f''(x) < 0, what can be said about the concavity of f(x)?

Back

f(x) is concave down.

Front

What is the relationship between f'(x) and f(x) when f'(x) > 0?

Back

f(x) is increasing.

Front

What is the significance of a critical point in the context of a function's graph?

Back

It may indicate a local maximum, local minimum, or an inflection point.

Front

How can you determine if a function is concave up using its second derivative?

Back

If f''(x) > 0, the function is concave up.