Let y = f (x) be a twice differentiable function such that f(1) = 2 ; f(2) = – 1 ; f(3) = 5 ; f(4) = – 3 and f(5) = 1. Find the minimum number of real roots of the equation f '(x)

Engineering

Mathematics

Rolles Theorem

Lagranges Mean Value Theorem

Question

Let y = f (x) be a twice differentiable function such that f(1) = 2 ; f(2) = – 1 ; f(3) = 5 ; f(4) = – 3 and f(5) = 1. Find the minimum number of real roots of the equation f '(x) · f '' (x) = 0.

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f (x) = 0 has atleast 4 real roots (IMVT)
f '(x) = 0 has atleast 3 real roots (Rolle's)
f "(x) = 0 has atleast 2 real roots (Rolle's)