Theorems

Question 1

Intermediate Value Theorem

Answer 1

If f(x) is continuous on [a,b] and y is in between f(a) and f(b), then there exists at least one value c on (a,b) such that f(c) = y

Question 2

Extreme Value Theorem

Answer 2

If f(x) is continuous on a closed interval [a,b], then there must be an absolute maximum and absolute minimum on [a,b].

Question 3

Rolle’s Theorem

Answer 3

If f(x) is continuous on [a,b], differentiable on (a,b) and f(a) = f(b), then there is guaranteed a value c on (a,b) such that f’(c) = 0

Question 4

Mean Value Theorem

Answer 4

If f(x) is continuous on [a,b] and differentiable on (a,b), then there is guaranteed a value c on (a,b) such that f’(c) = (f(a) - f(b))/(a - b)