Hi, I need to do this proof and i am very lost, Can anyone show me how to do it.
A function f(x) is said to be increasing at a point x0 in its domain if there exists some δ>0 such thatf(x)≥f(x0)forx0 ≤x≤x0+δ,andf(x)≥f(x0)for x0 − δ ≤ x ≤ x0. Using the definition of the derivative, show that if f′(x0) > 0, then f is increasing at x0, that is, there exists some δ > 0 such that the above inequalities hold.