Question

Find any relative extrema of the function.Use a graphing utility to confirm your result.

g (x) = x sech x

Answer 1

Step 1:

The function is .

Differentiate with respect to .

Find the critical number by equating to zero.

  can never be zero.

.

Substitute in .

The relative extrema  is .

Substitute in .

.

The relative extrema is .

Step 2:

Determine the nature relative extrema, using second derivative test.

Differentiate with respect to .

Recall the derivative formulae:

 

The function has relative maximum at .

The function has relative minimum at .

Step 3:

Graph:

Graph the function .

Observe the graph, the function has relative maximum at

And the function has relative minimum at .

Soluiton:

Relative maximum of the function is .

Relative minimum of the function is .