Question

Let $f\left(x\right)=x^2{e}^x$ then $f^{\prime \prime }\left(0\right)=$

• A. $1$
• B. $0$
• C. $2$
• D. $7$

Answer 1

Answer: (C)

$2$

Given,

$f\left(x\right)=x^2{e}^x$

Now differentiating both sides with respect to $x$ we get,

$f^{\prime }\left(x\right)=x^2{e}^x+2x{e}^x$

Again differentiating both sides with respect to $x$ we get,

$f^{\prime \prime }\left(x\right)=x^2{e}^x+4x{e}^x+2e^x$.

Now $f^{\prime \prime }\left(0\right)=2$.