A rectangle has its base on the x axis and its upper two vertices on the parabola y = 6 -x^2. What is the largest area the rectangle can have and what are its dimensions?

Question

campbell_st · Answer

ok... so the parabola looks like 


|dw:1428357836356:dw|

I assumed the rectangle is symmetrical about the y axis

and each vertical side is x units from the origin... so the width of the rectangle
is 2x

the length is f(x) 

so the area of the rectangle is 

$$A = 2x \times f(x) = 2x \times 6 - x^2$$

so 

$$A = 12x - 2x^3$$

I'd find the derivative and then solve for x