Question

Q3. Find a rectangle of largest area function f(x,y) = xy, that can be inscribed in the closed
region bounded by the x -axis, y -axis, and graph of y = 8 – x3.

Answer 1

A= xy

 

y= 8-x^3

 

A= x(8-x^3)= 8x-x^4

 

A' =8-4x^3 =0  (Take derivative and set equal to zero)

 

x= 2^(1/3)

 

A= xy  =  2^(1/3)  *(8-2)= 6*2^(1/3)  is largest area