10. give an example of a function that is increasing on one interval and decreasing on another. explain your…

Explanation:

Step1: Choose a quadratic function

Consider the function $y = x^{2}$.

Step2: Analyze its derivative

The derivative of $y = x^{2}$ is $y'=2x$. When $y'>0$, the function is increasing. Solving $2x>0$ gives $x > 0$. When $y'<0$, the function is decreasing. Solving $2x<0$ gives $x<0$.

Answer:

The function $y = x^{2}$ is decreasing on the interval $(-\infty,0)$ and increasing on the interval $(0,\infty)$.