SOLUTION: This is a calculus problem. Consider the graph of y= root x. There is some point on this graph that is closest to (4,0). What is the x-coordinate of that nearest point?

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Question 859045: This is a calculus problem. Consider the graph of y= root x. There is some point on this graph that is closest to (4,0). What is the x-coordinate of that nearest point?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

Use the distance formula to calculate the distance from (4,0) to any arbitrary point on the curve (x,y).
D%5E2=%28x-4%29%5E2%2B%28y-0%29%5E2
D%5E2=%28x-4%29%5E2%2By%5E2
From the function,
y=sqrt%28x%29
y%5E2=x
Substitute,
D%5E2=%28x-4%29%5E2%2Bx
D%5E2=%28x%5E2-8x%2B16%29%2Bx
L=D%5E2=x%5E2-7x%2B16
To minimize the distance,you can also minimize the distance squared. So take the derivative of the distance squared with respect to x and set it to zero.
dL%2Fdx=2x-7
2x-7=0
2x=7
x=7%2F2