Question

If a graph of $y=f\left(x\right)$ is symmetrical about the point $(5,0)$ and $f^{\prime }\left(7\right)=3$, then the value of $f^{\prime }\left(3\right)$ is

• A. $3$
• B. $0$
• C. $1$
• D. $Noneofthese$

Answer 1

The correct option is A $3$

As $f\left(x\right)$ is symmetrical about $(5,0)$

So, $f(5-k)=f(5+k)$

and $f^{\prime }(5-k)=f^{\prime }(5+k)$

$f^{\prime }\left(7\right)=f^{\prime }(5+2)=f^{\prime }(5-2)=3$

Hence,$f^{\prime }(5-2)=f^{\prime }\left(3\right)=3$