help!!- Applications of Differentiation?

Question

1. An open cardboard box is to be made by cutting squares of side x cm from each corner of a square of card of side 60 cm and folding the "resulting" flaps up to form the box. Find the value of x that will give the box the maximum volume

2. A body is projected from an origin o and moves in a straight line such that its displacement from 0, t seconds after projection is s metres where s=(t^3)/3-(6t^2)+50t. The velocity of the body is given by ds/dt. 
For what value of t is the body moving with the minimum velocity and how far from O is the body at that time? 

3. The curve y=ax^2 + b passes through the points A (3,39) and B (-2,c). The tangent to the curve at A is parallel to the line y-30x+7=0
Find a,b,c and the equation of the tangent to the curve at B

black cat · Accepted Answer

Yes, it differentiation
V = t(60-2t)^2 , so max is when x is around 40, you take the derivative set it equal to zero, find x and plug it in back in to v to find max v  - or use a graphing calculator and the trace button 

v (t) = the derivative of s(t)  so v(t) is t^2- 12 t +50; find when that is equal to zero and there's your time, plug it back into s of t and get the distance

for 3 here's my hint: take the derivative the curve; then plug in for x and set it equal to the slope of the parallel line; this will give you a; put a back into the original curve equation and use the point A to solve for b; then you have the equation; plug in the x value of point B to find  c

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help!!- Applications of Differentiation?

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