4.2

[1,4] original equation

find first derivative using quotient rule

first derivative equation

plug in c and simplify

use mean value theorem to find c

solved for

set equal

4.2

f(x) = x+ x –1 [0,2]

Since f is a polynomial, it is continuous and differentiable for all values x, including the values within the closed interval of [0,2].

(c) = 3c+1

(c) = = = 5

3c+1 = 5

3c= 4

c= c = c =

4.2

1.) equation is continuous on closed interval [0,2]

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

3.) f(a)=f(b)