Theorems

Question 1

Mean Value Theorem

Answer 1

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

Question 2

Newton’s Method

Answer 2

x(sub n+1)= x(sub n)- f(x(sub n))/ f’(x (sub n))

Used to approximate the root of f(x)=0

Question 3

Extreme Value Theorem

Answer 3

If f(x) is continuous on the closed interval [a,b], then there exists numbers c and d where f(c) is the absolute max and f(d) is the absolute min

Question 4

Intermediate Value Theorem

Answer 4

If f(x) is continuous on the closed interval [a,b] then there is one point c, if f(a) < f(c) < f(b) and a< c <b