Question

$f\left(x\right)$ is a polynomial of degree 2, $f\left(0\right)=4,f^{\prime }\left(0\right)=3$ and $f^{\prime \prime }\left(0\right)=4$, then $f(-1)$ is equal to

• A. 3
• B. -2
• C. 2
• D. -3

Answer 1

The correct option is A 3

Let, $f\left(x\right)=a{x}^2+bx+c$

$f\left(0\right)=4\Rightarrow 0+0+c=4\Rightarrow c=4$

$\therefore f\left(x\right)=a{x}^2+bx+4$

$f^{\prime }\left(x\right)=2ax+b\Rightarrow f^1\left(0\right)=3$

$\Rightarrow f^{\prime }\left(0\right)=0+b=3\Rightarrow b=3$

$\therefore f\left(x\right)=a{x}^2+3x+4$

$f^{\prime \prime }\left(x\right)=2a=4\Rightarrow a=2$

$\therefore f\left(x\right)=2x^2+3x+4$

$f(-1)=2(-1{)}^2+3(-1)+4=2-3+4=3$