Find the point on the graph of the function $f ( x ) = \sqrt { x } \text { that is closest to the }$ point $( 18,0 )$
A) $\left( \frac { 35 } { 2 } , \sqrt { \frac { 35 } { 2 } } \right)$
B) $\left( \frac { 37 } { 2 } , \sqrt { \frac { 37 } { 2 } } \right)$
C) $\left( \frac { 35 } { 2 } , \sqrt { \frac { 37 } { 2 } } \right)$
D) $\left( \sqrt { \frac { 37 } { 2 } } , \frac { 35 } { 2 } \right)$
E) $\left( \sqrt { \frac { 35 } { 2 } } , \frac { 35 } { 2 } \right)$

Question

Find the point on the graph of the function $f ( x ) = \sqrt { x } \text { that is closest to the }$ point $( 18,0 )$ 
A) $\left( \frac { 35 } { 2 } , \sqrt { \frac { 35 } { 2 } } \right)$
B) $\left( \frac { 37 } { 2 } , \sqrt { \frac { 37 } { 2 } } \right)$
C) $\left( \frac { 35 } { 2 } , \sqrt { \frac { 37 } { 2 } } \right)$
D) $\left( \sqrt { \frac { 37 } { 2 } } , \frac { 35 } { 2 } \right)$
E) $\left( \sqrt { \frac { 35 } { 2 } } , \frac { 35 } { 2 } \right)$

Quizplus · Accepted Answer

To find the point on $f(x) = \sqrt{x}$ closest to $(18,0)$, minimize the distance $d = \sqrt{(x-18)^2 + (\sqrt{x})^2}$. The derivative of $d^2$ with respect to $x$ gives the minimum at $x = \frac{35}{2}$, so the point is $\left( \frac{35}{2}, \sqrt{\frac{35}{2}} \right)$.

Find the Point on the Graph of the Function f(x)=x that is closest to the f ( x ) = \sqrt { x } \text { that is closest to the }f(x)=x​ that is closest to the

Find the Point on the Graph of the Function $f ( x ) = \sqrt { x } \text { that is closest to the }$