Casio ClassPad II Custom Commands

IMPORTANT - requires printpts stored in the same folder as your current folder or in the “library” folder (see the Variable Manager).

keypts(f, l, u)

• f is an expression in terms of x (execution of Program may partially fail if there are other unknown variables in the expression)
• l is the lower boundary of x (l should not be in terms of unknown variables)
• u is the upper boundary of x (u should not be in terms of unknown variables)

Prints and categorises coordinates of key points on y=f in the domain xϵ[l, u].

• y-axis intercepts where x=0
• x-axis intercepts where y=0
• stationary points where f \('\)=0
  • local minima where f \(''\)>0
  • local maxima where f \(''\)<0
  • stationary points of inflection where f \(''\)=0 and f \('''\)≠0
  • stationary points of unknown nature where f \(''\)=0 and f \('''\)=0 (users should verify the nature of these points themselves)
• points of inflection where f \(''\)=0 and f \('''\)≠0
• possible points of inflection where f \(''\)=0 and f \('''\)=0 (users should verify the nature of these points themselves)
• endpoints where x=l and x=u

The 2nd and 3rd derivative tests are not on the VCE Mathematical Methods Study Design.

Example

Find key points on \(y = \dfrac{1}{5} x^5 + \dfrac{3}{4} x^4 - 2x^2 + \dfrac{12}{5}\) for \(x \in (-\infty, 2]\).

Contributed by Nhan