Topic: Electronics Engineering
There is a function $f(x)$, such that $f(0)=1$ and $f^{\prime}(0)=-1$ and $f(x)$ is positive for all values of x, then
- A. $f^{\prime\prime}(x)<0$ for all x
- B. $-1<f^{\prime\prime}(x)<0$ for all x
- C. $-2<P^{\prime\prime}(x)<-1$ for all x
- D. None of these
Answer: D. None of these
Explanation: $f(x)=e^{-x}\Rightarrow f(0)=e^{-0}=1$
$f^{\prime}(x)=-e^{-x}\Rightarrow f^{\prime}(0)=-e^{-0}=-1$
$f(x)=e^{-x}is+ve~for\forall x$
$f^{\prime\prime}(x)=e^{-x}is+ve~for~\forall x$