Calc 1 theorems

What conditions are required for IVT (Intermediate Value Theorem)?

1. f(x) is continuous on [a,b] (closed interval)

2. f(a) DOES NOT EQUAL f(b)

What conditions are required for Rolle’s Theorem?

1. f(x) is continuous on [a,b] (closed interval)

2. f(x) is differentiable on (a,b) (open interval)

3. f(a) = f(b)

What conditions are required for Extreme Value Theorem?

1. f(x) is continuous on [a,b] (closed interval)

What conditions are required for Mean Value Theorem?

1. f(x) is continuous on [a,b] (closed interval)

2. f(x) is differentiable on (a,b) (open interval)

What does IVT indicate?

The function f will have every value between f(a) and f(b)

What does Rolle’s Theorem indicate?

f’(x) must equal zero at some point on [a,b]

What does MVT indicate?

AROC = f’(x) on [a,b] at some point

What does EVT indicate?

f(x) has a maximum and minimum value on the interval [a,b]