Question Type 3: Determining whether certain points are minimum and maximum by inspection through technology Exercises

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

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

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

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

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

By inspection via technology, determine whether the point $(e, f(e))$ is a local extremum for $f(x)=\frac{\ln(x)}{x}$, and state its nature.

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

Using a computer algebra system to graph $f(x)=\ln(x^2+1)-x$, determine the extremum at $x=0$ and classify it.

Using technology, classify the extremum at $x=-1$ for $f(x)=\frac{x^2e^x}{x-1}$.

Using technology, determine if $f(x)=\frac{x^3-3x+1}{x}$ 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 $f(x)=\frac{x^2e^x}{x-1}$.

With graphing technology, classify the extremum at $x=0$ for $f(x)=\frac{\sin x}{x}$ (for $x\neq0$, define $f(0)=1$).