An Increasing Function Meets Its Inverse
Difficulty: Medium · Topics: Calculus, Derivatives, Inverse Functions
O‘suvchi funksiya o‘z teskarisi bilan uchrashadi
f(x) is increasing and differentiable on the set of all real numbers. Let g(x) satisfy:
(i) g(x) is the inverse of f(x) and is differentiable.
(ii) lim x→ 2fracf(x)-g(x)(x^2-4)\g(x)+1\=2/9.
Find g'(2).
f(x) barcha haqiqiy sonlar to‘plamida o‘suvchi va differensiallanuvchi. g(x) quyidagilarni qanoatlantirsin:
(i) g(x) — f(x) ning teskarisi va differensiallanuvchi.
(ii) lim x→ 2fracf(x)-g(x)(x^2-4)\g(x)+1\=2/9.
g'(2) ni toping.