Question Type 2: Determining whether points satisfying the first order condition are local optimals Exercises

Find the stationary points of the function $f(x)=x^2e^x$ and determine whether each is a local minimum or maximum.

Find and classify the stationary points of the function $f(x)=(x-2)^2 e^{-x}$.

Find the stationary points of $f(x)=xe^{-x}$ and classify them.

Determine the stationary points of $f(x)=xe^{-x}+x$ and state their nature.

Find the stationary point of $f(x)=e^{-x}(x+2)$ and state its nature.

Determine the stationary point(s) of $f(x)=e^x(x-1)^2$ and state their nature.

Determine and classify the stationary points of $f(x)=\frac{x^2}{e^x}$.

Find and classify the stationary points of $f(x)=x^3e^{-x}$.

Determine the stationary point(s) of f(x)=rac{e^x}{x+1} and state whether each is a minimum or maximum.

Determine the stationary points of $f(x)=x^2e^{-x^2}$ and classify each.

Determine the stationary points of f(x)=rac{x^2e^x}{x-1} for $x\neq1$ and state their nature (min or max).

Find the stationary points of $f(x)=\frac{xe^x}{x^2+1}$ and determine their nature.