Let $A D$ and $B C$ be two vertical poles at $A$ and $B$ respectively on a horizontal ground. If $A D=8 \mathrm{~m}, B C=11 \mathrm{~m}$ and $A B=10 \mathrm{~m}$, then the distance (in meters) of point $M$ on $A B$ from the point $A$ such that $M D^2+M C^2$ is minimum, is

Question

Aicharya · Accepted Answer

$\begin{aligned} & f(x)=M D^2+M C^2 \ & \Rightarrow f(x)=x^2+8^2+(10-x)^2+11^2 \ & \Rightarrow f^{\prime}(x)=2 x-2(10-x) \ & \Rightarrow f^{\prime}(x)=4 x-20 \ & 	ext { for } f(x) 	ext { to be minimum } x=5\end{aligned}$

Let $A D$ and $B C$ be two vertical poles at $A$ and $B$ respectively on a horizontal ground. If $A D=8…

Solution