calc problem: rate of change of area of rectangle when x=12

[diedead]

A rectangle ABCD with sides parallel to the coordinate axes is inscribed in the region enclosed by the graph of y = -4x2+ 4 and the x-axis.a. Find the x- and y-coordinates of C so that the area of the rectangle ABCD is a maximum.b. The point C moves along the curve with its x-coordinate increasing at the constant rate of 2 units per second. Find the rate of change of the area of rectangle ABCD when x =12

please tell me how to start this problem and how to solve it through please

 

[galactus]

part a.

\(\displaystyle \L\\y={-}4x^{2}+4\) describes a parabola.

Let the area of the rectangle be A=2xy

Sub \(\displaystyle \L\\A=2x(-4x^{2}+4)=-8x^{3}+8x\)

Differentiate, set to 0 and solve for x

\(\displaystyle \L\\{-}24x^{2}+8=0\)

You can use the 2nd derivative test to check if it is indeed a max or min.