Question

On what interval/s is the following function increasing? f(x)=4x^3-5x^2-7x?

I think the answer is (1/12 15.44,,∞).

Answer 1

Step 1:

The function is .

Differentiate with respect to .

Find the critical number by equating to zero.

Roots of the quadratic equation are  .

Compare   with .

Substitute corresponding values in the

.

Step 2:

Critical points are .

Test intervals are .

The function is increasing on the interval and

and decreasing on the interval .

Solution:

The function is increasing on intervals and .