If f: R rightarrow R is an even function whic | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given that $f(x)$ is an even function,by definition,$f(x) = f(-x)$ for all $x \in R$. Differentiating both sides with respect to $x$,we get $f^{\p

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(C) Given that $f(x)$ is an even function,by definition,$f(x) = f(-x)$ for all $x \in R$. Differentiating both sides with respect to $x$,we get $f^{\prime}(x) = -f^{\prime}(-x)$. Differentiating again with respect to $x$,we get $f^{\prime \prime}(x) = f^{\prime \prime}(-x)$. This shows that the second derivative of an even function is also an even function. Since $f^{\prime \prime}(x)$ is an even function,$f^{\prime \prime}(-\pi) = f^{\prime \prime}(\pi)$. Given $f^{\prime \prime}(\pi) = 1$,it follows that $f^{\prime \prime}(-\pi) = 1$.

If $f: R \rightarrow R$ is an even function which is twice differentiable on $R$ and $f^{\prime \prime}(\pi)=1$,then $f^{\prime \prime}(-\pi)$ is equal to

Similar Questions

If $y=\sin (\log _e x)$,then $x^2 \frac{d^2 y}{d x^2}+x \frac{d y}{d x}$ is equal to

Perhydrol is an aqueous solution of

Rutherford’s scattering experiment is related to the size of the

From the ground state electronic configuration of the elements given below,pick the one with the highest value of second ionisation energy.

When the angle of incidence is $60^{\circ}$ on the surface of a glass slab,it is found that the reflected ray is completely polarized. The velocity of light in glass is

Vedclass Test Series

Exam Paper Generator

Online Exam Module