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Differentiation and Rate of Change Word Problems

1) Differentate the equations a) y=8/5xsquared b) y=4cosX - 3ex

2)The fomula C=60=t3/12 This equation refers to a machine in a workshop. This machine costs £C to lease each week according to the formula and t is the number of hours per week worked by the machine. The rate of increase of cost during the week is given by dC/dt.

a) Find a general expression for dC/dt.

b) use your expression to calculate after how many houre (t) the rate of increase of cost exceeds £1:50

3)Intergrate the following equations y = - 2/square rute of x3 and Y = x8 + x8/x8

4) s = 18 - 2t + 3.5t3 s = distance and t = seconds

1) find the equation for the acceleration, dv/dt ao the body

5) using you equation from above find the acceleration of tht body in m/s2 after the time 39.5 sec .

Solution Preview

Note: Many places, it is not very clear what you meant; I am giving you different answers based on what I can infer from your questions. This should cover all possiblities.

I will use the "^" for exponents; dy/dx for derivative
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1) Differentate the equations a) y=8/5xsquared b) y=4cosX - 3ex

Ans: a) Without proper paranthesis, there are two possibilities.

1) y = (8/5)* ...

Solution Summary

Rate-of-change word problems are solved.

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