How to do this Calc problem?

With the formula d=80+30cos(pie/3)t, Estimate the instantaneous rate of change of d with respect to t at t=1.5. Please explain how to do it.

Comments

  • well first you could just find the derivative and put 1.5 in then get the exact answer, but for estimation, take 2 points close to 1.5, so like t = 1.4 and 1.6, find the difference between those 2 values and divide by the difference in time.... 0.2s (I'm assuming seconds)

  • So

    The instantaneous rate of change is the derivative of d, which is:

    d'=-10pisin(pi/3t), when t=3/2, it is d'=- 10 pisin(pi/2)=-10 pi

  • Then,d'(1.5)=-30(pi/3)sin(pi/3)t=

    =-10pi * sin(pi/2)=-10pi

    God bless you.

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