Bonjour,
[tex]f(x) = \frac{2}{3}x^3- \frac{3}{2}x^2-2x+1\\\\
f'(x) = 2x^2-3x-2\\\\\\
f'(x) = 0 \Longleftrightarrow x= \frac{-1}{2} \qquad ou \qquad x=2 \\\\
f'(x) \ \textgreater \ 0 \Longleftrightarrow x\in ]-\infty; \frac{-1}{2}[U]2;+\infty[\\\\
f'(x) \ \textless \ 0 \Longleftrightarrow x\in ] \frac{-1}{2};2[ [/tex]
[tex]\lim_{x\to -\infty}f(x)=\lim_{\to -\infty} \frac{2}{3}x^3=-\infty\\\\
\lim_{x\to \infty}f(x)=\lim_{\to \infty} \frac{2}{3}x^3=\infty [/tex]
[tex]f( \frac{-1}{2})= \frac{37}{24}\\\\
f(2)= \frac{-11}{3} [/tex]
