Question

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

• A. 2
• B. 3
• C. 4
• D. 6

Answer 1

Answer: (D)

Correct answer is (d) 6