Area of rectangle = xy
= x�ã(4r^2 - x^2)
Take the derivative. I am having trouble with the algebra.
4 answers
x *(4r^2 - x^2)^-1/2
Sorry. I'm having trouble with the font. Here is the correct equation.
Area of rectangle = xy
=x *(4r^2 - x^2)^1/2
Area of rectangle = xy
=x *(4r^2 - x^2)^1/2
Using the product rule
d(area)/dx = x(1/2)(4r^2-x^2)^(-1/2)(-2x) + (4r^2-x^2)^(1/2)
= -x^2(4r^2-x^2)^(-1/2) + (4r^2-x^2)^(1/2)
= (4r^2-x^2)^(-1/2)[-x^2 + 4r^2-x^2]
= (4r^2 - 2x^2)(4r^2-x^2)^(-1/2)
you will probably set this equal to zero
to solve
4r^2 - 2x^2 = 0
etc
d(area)/dx = x(1/2)(4r^2-x^2)^(-1/2)(-2x) + (4r^2-x^2)^(1/2)
= -x^2(4r^2-x^2)^(-1/2) + (4r^2-x^2)^(1/2)
= (4r^2-x^2)^(-1/2)[-x^2 + 4r^2-x^2]
= (4r^2 - 2x^2)(4r^2-x^2)^(-1/2)
you will probably set this equal to zero
to solve
4r^2 - 2x^2 = 0
etc
Thank you. It makes so much sense now.