what point on the curve y=2sqrtx is closest to the point (4,0)?

Question

kainui · Answer

Draw a picture and then draw several lines between the point and other points on the curve. What do you notice? If you made the distance between the points as a hypotenuse of a right triangle, can you see how that if the triangle's function changes, its hypotenuse will only have one smallest point, which corresponds to the minimum of its graph?

anonymous · Answer

I kind of understand what you're saying but not clearly.

anonymous · Answer

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agent0smith · Answer

You have to use the distance formula, and find where it's a minimum.

anonymous · Answer

can you show me how to do that?

agent0smith · Answer

$$\Large d^2 =  (x-x_1)^2 + (y-y_1)^2$$x1 and y1 are the coordinates, (4,0)

x is just x, y is 2sqrtx.

Plug them all in, differentiate d^2 and set it equal to zero.