Question

Find all relative extrema. use the second Derivative Test where applicable.

f (x) = x^3 - 3x^2 + 3

Answer 1

Step 1:

The function is .

Apply derivative with respect to .

.

To find the relative extrema,solve .

Apply zero product property.

and .

and .

Hence, the critical values of  are and .

Step 2:

substitute in .

The point is .

Substitute in .

.

The point is .

The relative extrema points are and .

Comments

Contd...

Step 3:

Determine the relative extrema, using second derivative test.

Apply derivative 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 .