1. Tardigrade
  2. Question
  3. Mathematics
  4. Let f(x) be a cubic polynomial with leading coefficient unity such that f(a)=b and f prime(a)=f prime prime(a)=0. Suppose g(x)=f(x)-f(a)+(a-x) f prime(x)+3(x-a)2 for which conclusion of Rolle's theorem in [a, b] holds at x=2, where 2 ∈(a, b). The value of f prime prime(2) is equal to

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Q. Let $f(x)$ be a cubic polynomial with leading coefficient unity such that $f(a)=b$ and $f^{\prime}(a)=f^{\prime \prime}(a)=0$. Suppose $g(x)=f(x)-f(a)+(a-x) f^{\prime}(x)+3(x-a)^2$ for which conclusion of Rolle's theorem in $[a, b]$ holds at $x=2$, where $2 \in(a, b)$.
The value of $f ^{\prime \prime}(2)$ is equal to

Application of Derivatives

Solution:

Correct answer is (d) 6