Question

The landscaper has 12 feet of brick wall enclosed rectangular flower box. if the side of the house forms one side of the rectangle, (a) what is the maximum area of the floor box can enclose? (b) what dimensions of the box will yield this area?

Answer 1

we will find area in terms of single variable and maximize it by using derivative

For relative maximum or minimum

To maximize or minimize a function f(x) 1st we need to find its critical points

For critical points we need to put differentiation of f(x) equal to zero i.e. f '(x) = 0

Then check second derivative of f(x) i.e. f ''(x) is positive or negative at critical numbers If f ''(x) >0 then that gives minimum value of f(x) and if f ''(x) <0 then that give maximum value of f(x)