1. Your company is making dice (cubes) and speci-fications require

1. Your company is making dice (cubes) and speci-fications require
that their volume be 87±2 cm^3.How long should each side be and how muchvariation can be allowed?

2. The position s (in miles) of a particle is modeled by the following function of time t (in hours):
s(t)=t^4-8t^3+16t^2
Find the velocity and acceleration functions with respect to time. What is the velocity of this object at time t = 45 minutes?
What is the acceleration of this object at time t = 45 minutes?
Graph the position, velocity, and acceleration functions on the interval [0, 6]. Pinpoint when the object is moving forward
and when it is moving backward.
Give the time intervals in which the object is speeding up. Give the time intervals in which the object is slowing down.

3. A spherical balloon is inflated with helium at a rate of 110???? ft^3/min. How fast is the balloon’s radius increasing
when the radius is 4 ft?

4. Use analytic methods to find those values of x for which the given function is increasing and those values of x for which
it is decreasing.
f(x) = 2x^2 + 4x

Use implicit differentiation to find dy/dx and d^2y/dx^2.
6) xy – x + y = 5

please show work

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