Example of finding constants conditions on $y'$ and $y''$.

Thanks to one of my AP6 students for this solution :-)

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Show that $y=f(x)$ where $f(x)=x^{2n}-cx$ has NO points of inflection, where $n\ge 2 $ is a positive integer and $c\ne 0$ is a real number

 

Properties of curves depending on the sign of $y', y''$.

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Example of inlection point and equation of a tangent.

 

Challenge question: If $x^my^n=(x+y)^k$ where $m,n,k\in\mathbb{Z}^+$ show that $\dfrac{dy}{dx}=\dfrac{y((k-m)x-my)}{x(nx+(n-k)y)}$

 

Example of Differentiation - Implicit (LG Q10 Ex4-5)

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Poster - Differentiation Rules