Question

F:R—>R, f(x)=x³-6x²-36x+2,Determine intervals in which the given function are strictly increasing or strictly decreasing.

Answer 1

Dear student:

Given: f:R —>R

f(x)= x³-6x²-36x+2

For determining the intervals in which f is increasing and decreasing.

Find derivative of f(x)

then see the derivative in which f is positive and negative.

If it is positive then f is increasing

And if it is negative then f is decreasing.

See the attachment.

Answer 2

In the attachment I have answered this problem.

Concept:

If the derivative of f(x) is positive for all values of x in interval I then f(x) is strictly increasing in I.

If the derivative of f(x) is negative  for all values of x in interval I then f(x) is strictly decreasing in I.

See the attachment for detailed solution.