I know that in order for g to be increasing, its derivative must be positive. But, I have a hard time showing that its derivative is indeed positive.
Thank you!
2026-03-29 15:33:05.1774798385
If f is increasing, then show that g is also increasing
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Hint:
By the Fundamental theorem of Calculus $$g'(x)=\frac{1}{x}f(x)-\frac{1}{x^2}\int_{0}^{x}f(t)dt=\frac{1}{x^2}\int_{0}^{x}f(x)-f(t)dt.$$