If f(x) is twice differentiable polynomial function such tha... | MATH - ROLLE'S THEOREM, LAGRANGE'S MEAN VALUE THEOREM | SolveeIt | Solveeit

Today, August 23

Question

If f(x) is twice differentiable polynomial function such that f(1) = 1, f(2) = 4, f(3) = 9, then

A

f ¢¢(x) = 2 " xÎR

B

There exist at least one xÎ(1, 2) such that f ²(x) = 3

C

There exist at least one xÎ(2, 3) such that f ¢(x) = 5

D

There exist at least one xÎ(1, 3) such that f ²(x) = 2

Answer

There exist at least one xÎ(1, 3) such that f ²(x) = 2

Explanation

Solution

$\left. \ \begin{matrix} f(1) = 1 \\ f(2) = 4 \\ f(3) = 9 \end{matrix} \right\}$ ̃ f(x) = x², f ²,(x) = 2