If and are continuous on and differentiable on

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

f(x)

and

g(x)

are continuous on

[a,b]

and differentiable on

(a,b)

, prove that there exists

c\in(a,b)

such that

\left|\begin{array}{cc}f(a)&f(b)\\g(a)&g(b)\end{array}\right|=(b-a)\left|\begin{array}{cc}f(a)&f'(c)\\g(a)&g'(c)\end{array}\right|.