Question

nr pct de extrem ale functiei integrala de la 0 la x din e^-t (t+1)dt este

Answer 1

Răspuns:

Explicație pas cu pas:

$\displaystyle\int_0^xe^{-t}(t+1)dt=-e^{-t}(t+1)|_0^x+\int_0^xe^{-t}=-e^{-x}(x+1)+1-e^{-t}|_0^x=\\=-e^{-x}(x+1)+1-e^{-x}+1=-e^{-x}(x+2)+2\\f(x)=-e^{-x}(x+2)+2\\f'(x)=e^{-x}(x+2)-e^{-x}=e^{-x}(x+1)\\f'(x)=0\Leftrightarrow x+1=0\Rightarrow x=-1\\\texttt{This is to say , functia are un punct de extrem.}$