# Calculus (MVT of Integrals?)

• tdwp

## Homework Statement

Let f be a differentiable function defined for all x>=0 such that f(0)=5 and f(3)=-1. Suppose that for any number b>0, the average value of f(x) on the interval 0<=x<=b is (f(0)+f(b))/x

a. Find the integral of f(x) from 0 to 3.
b. Prove that f'(x)=(f(x)-5)/x for all x<0.
c. Using part b), find f(x)

## Homework Equations

(b-a)(f((ave)x))= the integral of f(x) from a to b

## The Attempt at a Solution

Part a is easy, I got 6 as my answer. I'm completely at a loss on how to do part b/c. If anyone would at least point me in the right direction, I would greatly appreciate it.

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Suppose that for any number b>0, the average value of f(x) on the interval 0<=x<=b is (f(0)+f(b))/x
Either you copied out the question wrong or the question asked doesn't make sense.

Argh, yes I did copy it wrong. It should be (f(0)+f(b))/2.

Use your "relevant equations" together with the given formula for the average of f over [0,b] to get an equation. Differentiate both sides of the equation.