Question

Fie f:(0;+8) ->R, f(x)=$2\sqrt{x}-3\sqrt[3]{x}$ . Aflati ecuatia tangentei la $G_{f}$ in punctul $x_{0}$=1

Answer 1

ecuatia este, prin definitie

y-f(1)=f'(1) (x-1)

f(1) =2-3=-1

f'(x)=(2/(2√x)-3*(1/3)x^(-2/3)=1/√x-1/∛x²

f'(1)=1-1=0

deci ecuatia este

y-(-1)=0

y+1=0

y=-1 ceea ce inseamna ca (1;-1) este un extrem local al functiei