Question

Derivata functiei inverse:

Answer 1

f(x)=x³+2x
f'(x)=(x³+2x)'=(x³)'+(2x)'=3x²+2
Valoare (f^-1)'(y0)=1/f'(x0).
In cazul de fata y0=3, dar y0=f(x0) si putem determina valoarea lui x0:
3=f(x0)
x0³+2x0=3
x0³+2x0-3=0
x0=1
f'(1)=3*1²+2=3+2=5
(f^-1)'(3)=1/f'(1)=1/5
Varianta E).