Find the x-coordinate of the point on the parabola $y = \sqrt { x }$ nearest to the point (4, 0).
A) $\frac { 7 } { 2 }$
B)4

C)3
D) $\frac { 3 } { 4 }$
E)
$\frac { 2 } { 7 }$
F)2
G)0

H)None of these

Question

Find the x-coordinate of the point on the parabola $y = \sqrt { x }$ nearest to the point (4, 0).
A) $\frac { 7 } { 2 }$ 
B)4
 
C)3
D) $\frac { 3 } { 4 }$ 
E)
$\frac { 2 } { 7 }$
F)2
G)0

H)None of these

Quizplus · Accepted Answer

To find the x-coordinate of the point on the parabola $y = \sqrt{x}$ nearest to the point (4, 0), we can use the distance formula. The distance $D$ between a point $(x, \sqrt{x})$ on the parabola and the point (4, 0) is given by:$$D = \sqrt{(x-4)^2 + (\sqrt{x}-0)^2}$$To minimize this distance, we minimize the square of the distance (to avoid dealing with the square root), which is:$$D^2 = (x-4)^2 + x$$Taking the derivative with respect to $x$ and setting it to zero to find the minimum gives:$$2(x-4) + 1 = 0$$Solving for $x$ gives:$$2x - 8 + 1 = 0$$$$2x = 7$$$$x = \frac{7}{2}$$Therefore, the x-coordinate of the point on the parabola nearest to the point (4, 0) is $\frac{7}{2}$.

Find the X-Coordinate of the Point on the Parabola y=xy = \sqrt { x }y=x​

Find the X-Coordinate of the Point on the Parabola $y = \sqrt { x }$