Question

f:R—>R, f(x)=x²-2x+5,Determine the intervals in which F is increasing and the intervals in which F is decresing.

Answer 1

Dear student:

Given:F:R—>R

f(x)=x²-2x+5

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.