Applications of Derivatives

Front

What does it mean if f"(x) > 0?

Back

The function f(x) is concave up at that point.

Front

What type of value does the function y = -4x² have?

Back

The function has a maximum value.

Front

What does it indicate if f'(x) < 0?

Back

The function f(x) is decreasing.

Front

What is the derivative of sin(x)?

Back

The derivative of sin(x) is cos(x).

Front

How can you determine the intervals where f(x) is increasing?

Back

Look for where f'(x) > 0.

Front

What is the relationship between the first derivative and increasing/decreasing functions?

Back

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

Front

What does f''(x) < 0 indicate about the function f(x)?

Back

The function f(x) is concave down at that point.

Front

What is the second derivative test used for?

Back

To determine the concavity of a function and locate inflection points.

Front

What is an inflection point?

Back

A point on the graph where the concavity changes.

Front

How do you find critical points of a function?

Back

Set f'(x) = 0 and solve for x.