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 ?>0 such thatf(x)?f(x0)forx0 ?x?x0+?,andf(x)?f(x0)for x0 ? ? ? 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 ? > 0 such that the above inequalities hold.
A function f(x) is said to be increasing at a point x0 in its domain if there exists some ?>0 such thatf(x)?f(x0)forx0 ?x?x0+?,andf(x)?f(x0)for x0 ? ? ? 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 ? > 0 such that the above inequalities hold.