SOLUTION: A rectangle is to be inscribed under the arch of the curve y=4cos(x/2) from x = - (pi)radians and x= (pi) radians. What are the dimensions of the rectangle with the largest area? M

Algebra ->  Probability-and-statistics -> SOLUTION: A rectangle is to be inscribed under the arch of the curve y=4cos(x/2) from x = - (pi)radians and x= (pi) radians. What are the dimensions of the rectangle with the largest area? M      Log On


   

Question 436794: A rectangle is to be inscribed under the arch of the curve y=4cos(x/2) from x = - (pi)radians and x= (pi) radians. What are the dimensions of the rectangle with the largest area? My professor wants me to work in radians and use Newton's method to find the zero of the first derivative.
Any help would be greatly appreciated.
I know the area and derivative is the following..
A= (2x)(4 cos (x/2)) = 8xcos (x/2)

dA/dx = 8 cos (x/2) - 4xsin(x/2)
I don't know what to do next when the equation is equal to zero.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Set it equal to zero and use Newton's method. A simpler way might be to rearrange some variables first:

dA%2Fdx+=+8+cos%28x%2F2%29+-+4x%2Asin%28x%2F2%29+=+0

8cos%28x%2F2%29+=+4x%2Asin%28x%2F2%29 Divide through by cos(x/2)

8+=+4x%2Atan%28x%2F2%29

2%2Fx+=+tan%28x%2F2%29

tan%28x%2F2%29+-+2x+=+0

Now just solve using Newton's method and your calculator. You will have to define a recursive sequence using an initial guess, as well as the function and the derivative of that function. Make sure your angles are set to radians.