IB Mathematics Applications & Interpretation Question Type 3: Determining Whether Certain Points Are Minimum and Maximum by Inspection Through Technology Exercises

Using a graphing tool, classify the extremum at $x=-1$ for $f(x)=x^3-3x+2$.

Using a graphing calculator, determine if $f(x)=x{e}^{-x^2}$ has a local extremum at $x=-\frac{1}{\sqrt{2}}$ and classify it.

Using technology, determine and classify the extremum at $x=1$ for $f(x)=\frac{1}{x}+x$.

Using a graphic display calculator, graph the function $f(x)=\ln (x^2+1)-x^2$. Determine the coordinates of the extremum at $x=0$ and classify its nature.

Using graphing software, determine whether $(1,f(1))$ is a local extremum for the function $f(x)=x^3-3x+2$, and classify this point.

Use your graphic display calculator (GDC) to determine whether the point $(e,f(e))$ is a local extremum for $f(x)=\frac{\ln (x)}{x}$, and state its nature.

With graphing technology, classify the extremum at $x=0$ for the function $f(x)=\{\begin{array}{ll}\frac{\sin x}{x}& x\ne 0\\ 1& x=0\end{array}$.

By inspecting the graph with technology, classify the extremum at $x=\frac{1}{\sqrt{2}}$ for the function $f(x)=x{e}^{-x^2}$.

Using technology, determine if $f(x)=\frac{x^2-3x+1}{x}$ has a local extremum at $x=1$ and classify it.

Using a graphing tool, determine whether $(0.5,f(0.5))$ is a local maximum or minimum for $f(x)=\frac{x^2{e}^x}{x-1}$.