Question

F:R⁺—>R⁺, f(x)=x log x,Determine intervals in which the given function are strictly increasing or strictly decreasing.

Answer 1

Dear student:

Given: R⁺—>R⁺

f(x)=xlog x

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:         1. If the derivative of f(x) is positive for all x in the interval  I then f(x) is increasing in I.         2. If the derivative of f(x) is negative for all x in the interval  I then f(x) is decreasing in I.           See the attachment for detailed solution.