Critical points

May answer key po ba kayo nito. Icheck ko lang po sana kung tama answers ko. Thank you po. Critical points/maxima and minima

y=4-6x+x²
y=(2x-1)²
y=2+12x-x³
y=x³-3x²-9x+20
y=x³-3x²+4x+5
y=x³-6x²+12x
y=x⁴+2x²+8x+3
y=16x+4x²-x⁴
y=x²(x-2)²
a³y=x⁴
9a³y=x(4a-x)³
a³y=x²(2a²-x²)
a³y=x³(4a-3x)
a⁵y=x⁴(3a²-2x²)

Fluid mechanics

A hollow sphere 6 in inside diameter is rotated on a cable at 100 rpm. If the cable is 6 ft long and makes an angle of 30 degrees with the horizontal, what is the pressure in the center of the sphere if it is full of water? what is the equivalent specific weight at that point?

Centroids and Centers of Gravity; Moments of Inertia

Modified True or False:
1. The intersection of the vertical lines at various single support and orientation of a rigid body may approximate the center of gravity of the body.
2. The vertical and horizontal coordinates of the intersection at any reference frame is the centroid of the body.
3. It is assumed that the body is laminar and non-homogenous to determine the centroid.