Question

use the graph to state the absolute and local min and max values, if any, of the function f.

http://imgur.com/PoYyFL6

Answer 1

Step 1 :

Definition of Critical point :

The graph of the function at which it has a cusp with vertical tangent.

Definition of local extrema :

Functions can have "hills and valleys"  places where they reach a minimum or maximum value.

Definition of absolute extrema :

The maximum or minimum over the entire function is called an "Absolute" or "Global" maximum or minimum.

There is only one global maximum (and one global minimum) but there can be more than one local maximum or minimum.

Observe the graph :

Critical points : (-2, -1), (-1, 1) and (0. 0).

Local minimum points : (-2, -1) and (0. 0).

Local maximum points : (-1, 1).

Absolute minimum : (-2, -1).

Absolute maximum : (-1, 1).

Solution :

Local minimum points : (-2, -1) and (0. 0).

Local maximum points : (-1, 1).

Absolute minimum : (-2, -1).

Absolute maximum : (-1, 1).