Differentiation

What is the method to find absolute maximum and minimum?

Solve for x in the 1st derivative.

What are test points used for in finding absolute extrema?

They are used within a given interval or at x-points.

What does f'(x) < 0 indicate in terms of extrema?

It indicates a minimum.

What does f'(x) > 0 indicate in terms of extrema?

It indicates a maximum.

What does it mean when a function is concave up?

The second derivative is positive.

What does it mean when a function is concave down?

The second derivative is negative.

How do you determine concavity using the second derivative?

Solve for x in the second derivative and plug in any number x into f"(x)

What do you do after solving for x in the second derivative?

Plug in x values to determine if the second derivative is less than or greater than zero.

How do you find relative maxima and minima?

Solve for x in the 1st derivative.

What do you do after finding x values from the 1st derivative?

Plug in x values to the 2nd derivative.

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

It indicates a relative minimum.

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

It indicates a relative maximum.