What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 3 − x^2?

Question

anonymous · Answer

Okay here is the answer

anonymous · Answer

Area = x * y 

We need to find our X, because the height is a function of X. 

You can divide this problem into 2 rectangles, each one to both sides of the y axis, and the "big" rectangle will be the sum of both. 

so, the rectangle will have area = x * (12 - x^2) 

you have to maximize it, so we differentiate it: 

d(area)/dx = 12-3*x^2 = 0. 

then x = 2 

the area would be 2*(12-4) = 16 

lets see if its maximum or minimum... if we choose x = 0, we would get a height o 12, but an area of 0, so its a maximum (without doing any derivative tests :D ) 

So the area of both rectangles would be 32 units squared

tmagloire1 · Answer

._. that wasn't even my problem. where did you get those numbers from

tmagloire1 · Answer

but ill try this way and see what i get

amistre64 · Answer

they used a different curve, but the process seems good enough.

tmagloire1 · Answer

i got 4! thanks for the process