Theorems

Question 1

Extreme Value Theorem

Answer 1

if f(x) is continuous on [a,b] then it has an absolute max and an absolute min

Question 2

The Intermediate Value Theorem

Answer 2

If f(x) is continuous on [a,b] and L is between f(a) and f(b) then f(c)= L for some c in between a and b

Question 3

Mean Value Theorem

Answer 3

1. If f(x) is continuous on [a,b]
2. f’(x) exists in (a,b)
   Then f’(c)= f(b)-f(a)/b-a

Question 4

Rolle’s Theorem

Answer 4

1. If f(a)=f(b)
2. f’(x) exists in (a,b)
3. f(x) is continuous on [a,b]
   Then f’(c)=0 for some c value in [a,b]

Question 5

Closed Interval Method

Answer 5

1. Find Critical Numbers
2. Evaluate f(Critical Numbers) and f(endpoints)
3. Largest f(x) value is maximum and smallest f(x) value is a minimumk