Question 1125369: Find the point on the graph of the function that is closest to the given point.
f(x) = sqrt(x − 7) , (19, 0)
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
A point on the graph of the function has coordinates (x,sqrt(x-7)).
To minimize the distance between that point and (19,0), we can minimize the square of the distance.
The square of the distance between (x,sqrt(x-7)) and (19,0) is
The minimum value of a quadratic function ax^2+bx+c is when x = -b/2a.
The value of x that gives the minimum distance between (x,sqrt(x-7)) and (19,0) is -(-37/2) = 37/2.
The point on the graph closest to (19,0) is (37/2,f(37/2)) = (37/2,sqrt(23/2)).
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