If f:[a,b]\rightarrow R be a continuous on [a,b] and differentiable on (a,b),then prove or disprove that there is some c\in(a,b) such that

 <br />
\int_a^{b}f(x)dx=f(a)(b-a)+f'(c)\frac{(b-a)^2}{2}<br />

In such questions one is required to assume some function for which conditions for Rolle's or LMVT are satisfied.What I want to know is how does one find such functions