Question Type 1: Finding the stationary points of specific functions by setting first derivatives to 0 Exercises

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

Determine the stationary points of $f(x) = \frac{x+1}{x-1}$.

Find the stationary points of $f(x) = x^4e^{-x}$.

Determine the stationary points of $f(x) = x^3e^{-2x}$.

Determine the stationary point of $f(x) = xe^{-x}$.

Find the stationary points of $f(x) = x^2\ln(x)$, $x>0$.

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

Determine the stationary points of $f(x) = 2x^4 - 8x^2 + 3$.

Find the stationary points of $f(x) = x^3 - 6x^2 + 9x + 1$.

Determine the stationary points of $f(x) = \frac{\ln(x)}{x}$ for $x>0$.

Find the stationary points of $f(x) = x^2e^x$.