- #1
chipotleaway
- 174
- 0
Homework Statement
Let f(x) be a continuous function on [a, b] and differentiable on (a, b). Using the generalised mean value theorem, prove that:
[tex]f(x)=f(c) + (x-c)f'(c)+\frac{(x-c)^2}{2}f''(\theta)[/tex] for some [tex]\theta \in (c, x)[/tex]
Homework Equations
Hints given suggest consdiering F(x) = f(x) - f(c) - f'(c)(x-c) and G(x) = (x-a)^2
(F and G and their derivatives are the functions that appear in the given mean value theorem)
The Attempt at a Solution
I don't have no clue as to how to proceed other than making the substitutions in the hints and plugging it into the MVT equation and hoping the function I'm after pops out but this doesn't seem right - especially for the number of marks it's worth (plus I'm not really getting anywhere with it anyway).