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 $f(x) = \begin{cases} \frac{\sin x}{x} & x \neq 0 \\ 1 & x = 0 \end{cases}$.

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

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 $f(x)=\frac{x^2e^x}{x-1}$.