#4: Other Theorems

Question 1

What is the mean value theorem?

Answer 1

If f is continuous over the interval [a,b] and differentiable over [a,b],
then a point c must exist within that open interval where the instanteous RoC = average RoC.

Question 2

What is the Mean Value Theorem (MVT)?

Answer 2

f’(c) = [f(b)-f(a)] / (b-a)

Question 3

What is the difference between IVT and MVT?

Answer 3

IVT: On a given interval, you will have a y-value @ the endpoints. Every y-value exists between these two values at least once.

MVT: On a given interval, the derivative (instantaneous RoC) must = avg RoC somewhere on said interval.