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math: rearrange rules to latest and tell people rules are good

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eggy 2020-10-20 17:37:22 -04:00
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@ -436,8 +436,21 @@ results in the equation of the derivative function. Direct substitution of $h$ w
f´(x)=4x f´(x)=4x
$$ $$
### Drawing derivative functions
If the slope of a tangent is:
- positive/negative, that value on the derivative graph is also positive/negative, respectively
- zero, that value on the derivative graph is on the x-axis
Points of inflection on the original function become maximum/minimum points on the derivative graph.
The derivative of a linear equation is always constant, and the derivative of a constant value is $0$..
### Derivative rules ### Derivative rules
These rules can be used in place of/to supplement finding derivative functions using first principles and are usually much faster to calculate.
The degree of a derivative is always the degree of the original function$-1$. The degree of a derivative is always the degree of the original function$-1$.
The **power rule** applies to all functions of the form $f(x)=x^n,x \in \mathbb{R}$, such that: The **power rule** applies to all functions of the form $f(x)=x^n,x \in \mathbb{R}$, such that:
@ -462,17 +475,6 @@ $$f´(x) = g´(x) + h´(x)$$
$$f(x) = 2x^2 + 3x$$ $$f(x) = 2x^2 + 3x$$
$$f´(x) = 4x + 3$$ $$f´(x) = 4x + 3$$
### Drawing derivative functions
If the slope of a tangent is:
- positive/negative, that value on the derivative graph is also positive/negative, respectively
- zero, that value on the derivative graph is on the x-axis
Points of inflection on the original function become maximum/minimum points on the derivative graph.
The derivative of a linear equation is always constant, and the derivative of a constant value is $0$..
## Resources ## Resources
- [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf) - [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)