Question

If f is defined by `f(x)= x^3 +2x^2 + x`, how do you find the value of x when the average rate of change of f on the interval `x=-1` to `x =2` is equal to the instantaneous rate of change on the interval from `x=-1` to `x=2`? The answer is x=0.786?

Answer 1

Ok, this is a good one!
Consider that the instantaneous rate of change is the derivative, `f'(x)`, while the average is the difference between two values (evaluated in `x=a and x=b`) of your function in an interval divided by the interva (`b-a`)l!!!