anonymous
  • anonymous
An isosceles triangle has base B and height H. Assuming its area remains constant, express the rate of change of the base with respect to the height.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
I'm getting -2A/h^2 Does that look right?
anonymous
  • anonymous
My reasoning: A= 1/2 b * h 2A = b * h b = 2A/h db/dh 2A/h = db/dh 2A * h^-1 = 2A * -h^-2 = -2A/h^2
anonymous
  • anonymous
Argh! Distributed wrongly.

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anonymous
  • anonymous
Right, but you don't differentiate Area...only height.
anonymous
  • anonymous
Or am I wrong about this?
anonymous
  • anonymous
Doesn't it mean that if we keep the Area constant, at what rate does the base change respective of the height? That can't be 0, I wouldn't think.
anonymous
  • anonymous
A solution using Mathematica is attached.
anonymous
  • anonymous
I think I made a mistake.
anonymous
  • anonymous
yes, -2A/h^2 is the correct answer.
anonymous
  • anonymous
Thanks very much!

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