Question

Let a, b, c be three real numbers such that a < b < c. Let f(x) be continuous $\forall x\in [a,c]$ and differentiable $\forall x\in (a,c)$.If $f"\left(x\right)>0\forall x\in (a,c)$ then

• A. (c – b) f(a) + (b – a) f(c) > (c – a) f(b)
• B. (c – b) f(a) + (a – c) f(b) < (a – b) f(c)
• C. f(a) < f(b) < f(c)
• D. none of these

Answer 1

The correct option is A (c – b) f(a) + (b – a) f(c) > (c – a) f(b)

By LMVT
$\frac{f\left(b\right)-f\left(a\right)}{b-a}>\frac{f\left(c\right)-f\left(b\right)}{c-b}$