Explain and show work please Find the point on the line y = 6x + 9 that is close

Question

Explain and show work please

Find the point on the line y = 6x + 9 that is closest to the point (-3, 1) Clearly state the domain of the function that you optimize. Instead of minimizing the distance d, you may minimize d2 as it is easier. Sketch a graph of y = -x2 + 4 by sketching appropriate rectangles, illustrate the Riemann sum with three left-endpoint rectangles that approximates the area under the graph of y = -x2 + 4 between a = -1 and b = 2. Calculate this summation and the compare it to the exact value of (-x + 4)dx.

Explanation / Answer

6) d^2 = (x+3)^2 + (y-1)^2

y = 6x + 9

so z=d^2 = (x +3)^2 + (6x+8)^2

dz/dx = 2(x+3) + 2(6x+8)*6=0

x= -51/37

so y = 27/37

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