Question Type 1: Finding intervals where a function is increasing or decreasing Exercises

Determine the intervals of increase and decrease for $f(x)=\frac{x}{x^2+1}$.

Determine intervals of increase/decrease for $f(x)=xe^{-x}$ on $[0,\infty)$.

Find the intervals of increase and decrease for $f(x)=x^4-4x^3+4x^2$.

Determine where $f(x)=3x^3-9x+2$ is increasing or decreasing.

Determine the intervals of increase and decrease for $f(x)=\cos x$ on $[0,2\pi]$.

For $f(x) = \sin x$ on $[0, 2\pi]$, find the intervals where $f$ is increasing or decreasing.

Determine the intervals on which $f(x)=x^3-5x^2+6x+9$ is increasing and decreasing.

Find the intervals where $f(x)=\frac{1}{(x-1)^2}$ is increasing and decreasing for $x \in \mathbb{R}, x \neq 1$.

Find where $f(x)=\ln x - x$ is increasing and decreasing for $x>0$.

Find the intervals of increase and decrease for $f(x)=x^4-2x^2+1$.

Find the intervals on which the function $f(x) = x^3 + x^2 - x + 5$ is increasing or decreasing.

Determine intervals of increase and decrease for $f(x)=\sqrt{x}\ln x$ on $(0,\infty)$.