Quandaries and Queries
Subject: maxima problem
Who is asking: Student
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
3^(1/2) = xy + ------ y^2 *1* 4Given:
2x + 3y = 300
x = 50y *2*
Sub *2* into *1*
3^(1/2) A= 50y^2 + ------- y^2 4For maximum,
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,
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.Cheers,