IB Mathematics Applications & Interpretation Question Type 2: Determining Whether Points Satisfying the First Order Condition Are Local Optimals Exercises

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

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

Determine the stationary points of $f(x)=\frac{x^2{e}^x}{x-1}$ for $x\ne 1$ and state their nature (minimum or maximum).

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

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

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 the function $f(x)=(x-2{)}^2{e}^{-x}$.

Find the stationary points of $f(x)=\frac{e^x}{x^2-3}$ and determine their nature.

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

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

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