Subject: maxima problem

Name: evelina

Who is asking: Student
Level: Secondary

Question: Hi, I'm having troubles with taking the derrivative in this maxima problem.

Here's the actual question and my work so far...

A window is the shape of a rectangle with an equilateral triangle on top. The perimeter of the window is 300 cm. Find the width that will let the maximum light to enter.

 
   /\	   let y be the length of the
y /  \ y   sides of the triangle and
 /____\	   width of the rectangle in cm
 |  y  |   let x be the length of the
 |     |    rectangle in cm
x|     | x
 |_____|
    y
    

Maximize:

Area= (area of rectangle) + (area of triangle)

       3^(1/2)
= xy + ------ y^2   *1*
          4

Sub *2* into *1*

           3^(1/2)
A= 50y^2 + ------- y^2
              4

 dA
---- = 0
 dy
 
 dA
---- = 100y + ????
 dy
 

This is where my problem is. I cannot figure out how to take the derrivative of the square root of 3 etc. I've come up with many different answers but I know none of them work, when I set the derivative equal to zero I always get y to equal zero. Did I set up the problem incorrectly or is my problem just not knowing how to take the derrivative?

Thanks so much for your time,
Evelina

The square root of 3 divided by 4 is a constant just like 50 is a constant so if

The rreason that this answer "doesn't work" is that there is an error in your equation *2*. Since the perimeter is 300 cm you have correctly that

Substitite this equation *2* into *1* and differentiate.

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