Question Type 2: Finding the FOC for functions using technology Exercises

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

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

Find the FOC of $f(x)=\sin x + x$ and identify the stationary points in $[0,2\pi]$.

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

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

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

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

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

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

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

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

Determine the FOC for $f(x)=\displaystyle\frac{\ln x}{x}$, $x>0$, and find its stationary point.