Determine the Special Points of a Function - Maple Help

Determine the Special Points of a Function

 Description Find the asymptotes , critical points , extreme points , points of inflection , and roots  of a univariate function.

Define a univariate function

 > $f:={x}\to \left(\frac{{2}{{x}}^{{2}}{+}{3}{x}{-}{2}}{{{x}}^{{3}}{-}{2}{{x}}^{{2}}{-}{15}{x}}\right)$
 ${f}{:=}{x}{→}\frac{{2}{}{{x}}^{{2}}{+}{3}{}{x}{-}{2}}{{{x}}^{{3}}{-}{2}{}{{x}}^{{2}}{-}{15}{}{x}}$ (1)

Find the asymptotes of the function.

 > $\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{Asymptotes}\right]\left(f\left(x\right)\right)$
 $\left[{y}{=}{0}{,}{x}{=}{-}{3}{,}{x}{=}{0}{,}{x}{=}{5}\right]$ (2)

Find the critical points of the function.

 > $\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{CriticalPoints}\right]\left(f\left(x\right)\right)$
 $\left[{-}{3}{,}{0}{,}{5}\right]$ (3)

Find the extreme points of the function.

 > $\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{ExtremePoints}\right]\left(f\left(x\right)\right)$
 $\left[{}\right]$ (4)

Find the points of inflection of the function.

 > $\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{InflectionPoints}\right]\left(f\left(x\right)\right)$
 $\left[{-}{3}{,}{0}{,}{5}\right]$ (5)

Find the roots of the function.

 > $\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{Roots}\right]\left(f\left(x\right)\right)$
 $\left[{-}{2}{,}\frac{{1}}{{2}}\right]$ (6)