Let ?(?)=12?2f(x)=12x2. (a) If we wish to find the point ?=(?0,?0)Q=(x0,y0) on the graph of ?(?)f(x)...

Let ?(?)=12?2f(x)=12x2.

(a) If we wish to find the point ?=(?0,?0)Q=(x0,y0) on the graph of ?(?)f(x) that is closest to the point ?=(4,1)P=(4,1), what is the objective function? (Hint: optimize the square of the distance from ?P to ?Q.)

Objective function: ?(?)=O(x)=____________________________

(b) Find the point ?=(?0,?0)Q=(x0,y0) as described in part (a). Box your final answer.

(c) Verify that the line connecting ?P to ?Q is perpendicular to the line tangent to ?(?)f(x) at ?Q. Hint: recall that the lines ?=?1?+?1y=m1x+b1 and ?=?2?+?2y=m2x+b2 are perpendicular if ?1=−1?2m1=−1m2 (assuming neither are horizontal or vertical).

Expert Solution

milcah answered 2 years ago

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