Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · medium
Find the point on the curve y=x2 that is closest to the point (3,0).
- (1,1)
- (0,0)
- (3,9)
- (2,4)
Answer
A. (1,1)
Solution
Minimize D2=(x-3)2+x4. d(D2)/dx=2(x-3)+4x3=0 2x3+x-3=0, which factors as (x-1)(2x2+2x+3)=0. The quadratic factor has no real roots, so x=1, y=1.
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