Three Conditions Fixing a Function
Difficulty: Hard · Topics: Calculus, Integration, Derivatives
Funksiyani aniqlaydigan uchta shart
A function f(x), differentiable for every real x, satisfies all of the following conditions. Find the value of f(3). (Here a and b are constants.)
(a) f(x)= ∫ 0^x(t-a)e^ t-b dt
(b) The function f(x) has an extremum at x=1.
(c) f(2)-2f(0)=dfrac2e^3
Har bir haqiqiy x uchun differensiallanuvchi f(x) funksiya quyidagi barcha shartlarni qanoatlantiradi. f(3) ning qiymatini toping. (Bu yerda a va b — o‘zgarmaslar.)
(a) f(x)= ∫ 0^x(t-a)e^ t-b dt
(b) f(x) funksiya x=1 da ekstremumga ega.
(c) f(2)-2f(0)=dfrac2e^3