Question

Asked Nov 10, 2019

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Step 1

**Rolle's theorem** states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

Given f(x)=0 has n distinct solutions. Let, x1 , x2 , x3 , x4 , ...... , xn

Then, f(x1)= f(x2) = f(x3) = f(x4) = .... =f(xn)=0

Step 2

Since, f(x1)=f(x2)=0 so by Rolle's theorem f′(p1) = 0 for some p1 with x1 ≤ p1 ≤ x2. (There can be more than one point p1)

Since, f(x2)=f(x3)=0 so by Rolle's theorem f′(p2) = 0 for some p2 with x2 ≤...

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