find all relative extrma. use the second derivative test where applicapble

Question

g(x)=x^3-3x-10

Answer 1

Step 1:

The function is .

Apply derivative on each side with respect to .

.

Find the relative extrema by equating .

.

Hence, the critical values of  are and  .

Substitute in .

.

The point is .

Substitute in .

.

The point is .

The relative extrema points are and .

Step 2:

Using second derivative test, determine the nature of relative extrema.

Apply derivative on each side with respect to .

.

Point
Sign of
Conclusion	Relative maximum	Relative minimum

The relative maximum at .

The relative minimum at .

Solution:

The relative maximum at .

The relative minimum at .