Posted by Ifi on Sunday, October 28, 2012 at 4:13am.
Let f(x) be the parabola x^2+16x16. find the point (x,y) on f such that tangent line to f at (x,y) passes through the origin.
My ans is (8,48). First i do f'x then i find x and lastly i find y. I do this because the max/min point is the point where tangent line pass through. Pls correct me if im wrong.

Math  Steve, Sunday, October 28, 2012 at 6:04am
No, (8,48) is the max, so the tangent there is horizontal. It will not pass through the origin.
f'(x) = 2x+16
you want to find (h,k) where the line joining (0,0) and (h,k) has slope 2h+16
k/h = 2h+16
But, k = h^2+16h16, so
h^2+16h16 = h(2h+16)
h^2 + 16h  16 = 2h^2 + 16h
h^2  16 = 0
h = 4,4, so k = 32,96
The points are thus (4,96) and (4,32)
Check:
f'(4) = 8 = 32/4
f'(4) = 24 = 96/4
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