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Problem: Let y=f(x)be a differentiable function and let P(x0,y0)be a point that is not on the...

Problem: Let y=f(x)be a differentiable function and let P(x0,y0)be a point that is not on the graph of function. Find a point Q on the graph of the function which is at a minimum distance from P.

Complete the following steps. Let Q(x,y)be a point on the graph of the function

  1. Let D be the square of the distance PQ¯. Find an expression for D, in terms of x.
  2. Differentiate D with respect to x and show that f′(x)=−x−x0f(x)−y0
  3. The solution sought satisfies the equation obtained in step 2. The equation may be solved analytically or by the zero method of your graphing calculator.

Now apply the procedure to obtain the point on y=x2that is closest to the point

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