IB Mathematics Applications & Interpretation Question Type 2: Finding the FOC for Functions Using Technology Exercises

Find the stationary points of $f(x)=x^5-5x+3$.

Find the derivative of $f(x)=\sin x+x$ and identify the stationary point(s) in the interval $[0,2\pi ]$.

Determine the $x$-coordinates of the stationary points of $f(x)=\frac{x^2{e}^x}{x-1},x\ne 1$.

Find the first order condition (FOC) for the function $f(x)=\frac{e^x}{x-1}$ and determine its stationary point.

Determine all stationary points of $f(x)=x^4-4x^3+6x^2-4x+1$.

Determine the first-order condition for $f(x)=x{e}^x$ and find its stationary point.

Determine the first derivative of $f(x)=\frac{\ln x}{x}$, $x>0$, and find the coordinates of the stationary point.

Find the stationary points of $f(x)=x^2\sin x$ on $[0,\pi ]$.

Determine the first-order conditions for $f(x)=x^3-3x^2+2$ and find all stationary points.

Find the stationary point of $f(x)=x\ln x-x$ for $x>0$.

Find the stationary point of the function $f(x)=3x^2+2x-5$.

Find the stationary points of $f(x)=\ln (x^2+1)$.