Exercise 1.5 (Cauchy Mean Value Theorem) Let f(x) and g(x) be continuous on [a, b] and differentiable in

(a, b). Prove that there exists a point c in

(a,

b) such that

Hint: For g

(b) ̸= g(a), consider the function

Transcribed Image Text:

f(c)[g(b)g(a)] = g'(c)[f(b) f(a)]. -