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Minimizing F(x)

Let Q=(0,7) and R=(10,11) be given points in the plane. We want to find the point P=(x,0) on the x-axis such that the sum of distances PQ+PR is as small as possible.
To solve this problem, we need to minimize the following function of x. F(x)=?? over the closed interval [a,b] where a=?? and b=??

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Solution Preview

Distance between two points is sqrt[(x1-x2)^2+(y1-y2)^2]
<br>PQ = sqrt[(x-0)^2+(0-7)^2] = sqrt(x^2+49)
<br>PR = ...