How do you determine if rolles theorem can be applied to #f(x)=x^2-3x+2# on the interval [1, 2] and if so how do you find all the values of c in the interval for which f'(c)=0?
1 Answer
Apr 30, 2015
Rolle's theorem says that if a function f(x) is continuous in the closed interval [a,b] and differentiable in the open interval (a,b) and if f(a) = f(b), then there exists a point c between a and b such that f '(c)=0
The given function has f(1)= 1-3+2=0 and f(2)= 4-6+2 =0 and f(x) is continuous in [1,2] and it is also differentiable in (1,2). The conditions of Rolle's theorem are satisfied, hence f'(x) = 2 x -3 equated to 0 would give c.
Accordingly, 2 x-3=0 would give x=3/2 Hence at c=3/2 or 1.5
