INSTANTANEOUS RATE OF CHANGE PROBLEM

Question

anonymous · Answer

deatils?

anonymous · Answer

$$\int\limits_{0}^{x^2}sint dt$$

anonymous · Answer

Left f(x) = see above.  At how many points in the closed interval o to root pi does the instantaneous rate of change of f equal the average rate of change of f on that interval?

precal · Answer

That is an integration problem.  Instantaneous rate of change is usually derivatives.

anonymous · Answer

-cost+C

anonymous · Answer

I understand the integration part but how do you compare the rates of change?

precal · Answer

Derivatives and Antiderivates are inverses.  Recall integration is an antiderivate except it has an interval (in this case 0 to x^2) .  Those numbers are also limits.
Example addition and subtraction are inverses because one undoes the other.