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)

Help please :( - Flange Bolt coupling

A flanged bolt coupling consists of two concentric bolt circles. One bolt circle consists of six 0.5-in-diameter steel bolts on a circle 9 inches in diameter and the other consists of eight 0.5-in-diameter steel bolts on a circle 12 inches in diameter. What is the shearing stress in the bolts if a torque of 7 kip-ft is to be carried by the assembly?

Moment Area theorem problem. please help

I've been trying to solve the following question for 2 days now and i can't seem to be able to. can someone help me please ?

For the beam shown in Figure 3, the support at A is fully fixed. The beam is tapered however you may consider it to be a beam of 3 varying sections.

Take:
Beam A to B as having 3 times the I value of beam D to end, Beam B to D as having 1.5 times the I value of beam D to end and Beam D to end is 310 UB 46.2 with I = 100 x 106 mm4. Tip: this may be easier to solve using superposition.

Algebra

A 1,260-galloon tank is filled by two pipes in as many as the smaller pipe brings in galloons per minute. How long will it take each pipe to fill the tank if the larger pipe brings in one galloon per minute more than the smaller pipe?

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?