Function Expression :
\[f(x)=cos^3(x )-\frac{3}{2}cos(x ) \]Domain
\[]-\infty ;+\infty [ \]Limits
\[\lim_{x \rightarrow-\infty}f(x) = \left\langle - \frac{5}{2}, \frac{5}{2}\right\rangle \]\[\lim_{x \rightarrow+\infty}f(x) = \left\langle - \frac{5}{2}, \frac{5}{2}\right\rangle \]
\[ \]
Derivate
\[f^{\,\prime}(x)=- 3 \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{2} \]\[f^{\,\prime}(x)=- \frac{3 \sin{\left(x \right)} \cos{\left(2 x \right)}}{2} \]
\[ \]
Integral
\[F(x) = - \frac{\sin^{3}{\left(x \right)}}{3} - \frac{\sin{\left(x \right)}}{2} \]Sign Table
Variation Table
Plot
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