Posted by Anonymous on Thursday, January 24, 2008 at 9:54pm.
An isosceles triangle, whose base is the interval from (0,0) to (c,0), has its vertex on the graph of f(x)=12x^2. For what value of c does the triangle have maximum area?

Calculus  Reiny, Thursday, January 24, 2008 at 10:32pm
Let A(a,12a^2) be the point of the triangle which lies on the parabola.
Since it must be an isosceles triangle, c = 2a
The area of the triangel = 1/2(c)(12a^2)
=1/2(2a)(12a^2)
=12a  a^3
Then d(Area)/da = 12  3a^2
= 0 for a max area
3a^2 = 12
a = + 2, c = 2a
so c = 4
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