Let Q = (0, 2) and R=(7,5) be given points in the plane. We want to...

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Let Q = (0, 2) and R=(7,5) 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 P Q + P R is as small as possible. (Before proceeding with this problem, draw a picture!) 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 = . We find that f (x) has only one critical number in the interval at x = where f(x) has value Since this is smaller than the values of f (x) at the two endpoints, we conclude that this is the minimal sum of distances. Let Q = (0, 2) and R=(7,5) 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 P Q + P R is as small as possible. (Before proceeding with this problem, draw a picture!) 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 = . We find that f (x) has only one critical number in the interval at x = where f(x) has value Since this is smaller than the values of f (x) at the two endpoints, we conclude that this is the minimal sum of distances.

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