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

In recombinant $DNA$ technique,the term vector refers to

Two of the lines represented by the equation $a y^4+b x y^3+c x^2 y^2+d x^3 y+e x^4=0$ will be perpendicular,then

$A$ line is at a constant distance $c$ from the origin and meets the coordinate axes in $A$ and $B$. The locus of the centre of the circle passing through $O, A, B$ is

Which of the following is a fossil plant?

Which of the following is the strongest reducing agent?

Vedclass Test Series

Exam Paper Generator

Online Exam Module