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Calculus : Acceleration, Average Value and Values of Derivatives

8) The acceleration at time t, of a particle moving along the x axis is given by a(t)=20t^3+6. At time t=0 the velocity of the particle is 0 and the position of the particle is 7. What is the position of the particle at time t?

12) The function f is given by f(x)=3x^2+1. What is the average value os f over the closed interval [1,3]?

14) Selected values of function f and g and their derivatives, f' and g' are given in the table If h(x)=f(g(x)), what is h'(30)?

x f(x) f'(x) g(x) g'(x)
10 35 15 6 4
20 8 5 12 10
30 24 25 20 10

Solution Preview

8. Suppose the position is s(t), velocity is v(t). We know s'(t)=v(t) and v'(t)=a(t)=20t^3+6. Thus v(t)=5t^4+6t+C. When t=0, v(0)=0. So C=0 and v(t)=5t^4+6t. ...

Solution Summary

Problems involving acceleration, average value and values of derivatives are solved.