Here's the info: Suppose f(x) is a differentiable function on the interval [a,b]. Let y=mx+b be the line passing through the points (a, f(a)) and (b, f(b)). Suppose that f(x) intersects y exactly 4 times.
Use the Mean Value Theorem to prove that there exists at least three values of c such that the instantaneous rate of change at c equals the average rate of change on [a,b]
(Phew, that's a mouth full)
So I tried just showing that the slope at any point is equal to the diffinition of average slope, but my teacher didn't go for it. Late he hinted that we need to use three different points and then use the MVT three different times but I'm confused as to what points I'm supposed to use exactly.
Please help!