Homework Help Forum: Calculus - maximum problem

Posted by calculus on Monday, October 26, 2009 at 6:27pm.

An isosceles trapezoid is inscribed under the graph oof y =cos x. what are the dimensions which will give the greatest area?

• Calculus - maximum problem - Reiny, Monday, October 26, 2009 at 7:33pm

  I will assume you want the base to be on the x-axis. Let's make the base as long as possible, that is, from (-pi/2,0) to (pi/2,0) Let the other point of contact be (x,y) Area of trap = (1/2)(pi + 2x)(y) = (1/2)(pi+2x)cosx = (1/2)picosx + xcosx d(Area)/dx = (-1/2)pi(sinx) + x(-sinx) + cosx = 0 for a max/min of Area -pi(sinx) - 2xsinx + 2cosx = 0 2cosx = sinx(pi + 2x) 2/(pi + 2x) = tanx I ran this through a primitive Newton's Method program and got x = .45797

  
  

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