diff --git a/docs/mhf4u7.md b/docs/mhf4u7.md index 74d53ed..4a63059 100644 --- a/docs/mhf4u7.md +++ b/docs/mhf4u7.md @@ -545,6 +545,23 @@ When solving for questions that ask for rate of change related to other rates of - apply derivative rules (especially the chain rule) to every variable that is not a constant (i.e., that changes with respect to time) - substitute values only at the end +## 5.2 - Increasing and decreasing functions + + - If $f´(x) > 0$ in the interval $[a,b]$, $f$ is **increasing** on $[a,b]$. + - If $f´(x) < 0$ in the interval $[a,b]$, $f$ is **decreasing** on $[a,b]$. + - If $f´(x) = 0$ in the interval $[a,b]$, $f$ is **constant** on $[a,b]$. + - The points where $f´(x)=0$ are the **critical**/maximum/minimum points. + +Function only change whether they are increasing/decreasing/constant at the **critical points**/"relative extrema". + +These points and whether the intervals between them increase/decrease can be found by using an **interval chart/line** using the first derivative. + +!!! example + If $f(x)=\frac{2x-3}{x^2+2x-3}$: + + - $f$ is decreasing on $(-∞, -3) \cup (-3, 0) \cup (3, ∞)$. + - $f$ is increasing on $(0, 1) \cup (1, 3)$. + ## Resources - [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)