Question

Let $f\left(x\right)$ be a twice differentiable function for all real values of $x$ and satisfies $f\left(1\right)=1$, $f\left(2\right)=4$, $f\left(3\right)=9$. Then which of the following is definitely true?

• A. $f^{\prime \prime }\left(x\right)=2$ for all $x\in (1,3)$
• B. $f^{\prime \prime }\left(x\right)=f\left(x\right)=5$ for some $x\in (2,3)$
• C. $f^{\prime \prime }\left(x\right)=3$ for all $x\in (2,3)$
• D. $f^{\prime \prime }\left(x\right)=f^{\prime \prime }\left(x_0\right)$

Answer 1

The correct option is A $f^{\prime \prime }\left(x\right)=2$ for all $x\in (1,3)$

from values of function we can guess the function
$f\left(x\right)=x^2$
$f^{\prime \prime }\left(x\right)=2$
so answer is A