Sample E question

Ex 4-10B

 

Tutorial 23/6/23 Q5.10 Ex4-10A - Maximum/Minimum problems

Thanks to the two students for these solutions

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Extra differentiation exercises + quick quiz

  https://www.kutasoftware.com/freeica.html

For more exercises on differentiation (very very important to get this skill right now!!)

Basic powers, constants

https://cdn.kutasoftware.com/Worksheets/Calc/03%20-%20Power%20Constant%20and%20Sum%20Rules.pdf

Second order derivatives - $y''$

https://cdn.kutasoftware.com/Worksheets/Calc/03%20-%20Higher%20Order%20Derivatives.pdf

Product Rule

https://cdn.kutasoftware.com/Worksheets/Calc/03%20-%20Product%20Rule.pdf

Quotient Rules

https://cdn.kutasoftware.com/Worksheets/Calc/03%20-%20Quotient%20Rule.pdf

Chain Rule

https://cdn.kutasoftware.com/Worksheets/Calc/03%20-%20Chain%20Rule.pdf

Quiz - Test Yourself Now!!

In an exam, these are 1 mark each, answer does not have to be simplified here as we are not using it directly. But its still a good exercise to factorise.

Quick Quiz

Show me your answers and working in class please.

Asymptote examples - H.A., V.A., O.A., C.,A.

 

Ex4-9D Q5 curve sketch example

 

Calculus Brief Summary

 Calculus Brief Summary

Summary - Basic Differentiation Rules

  Summary - Basic Differentiation Rules

Tutorial w11T4 - sketch rational fns, some questions (ex4-9C)

 

Challenge question: Product Rule example with factorisation! If $y=x^m(bx-c)^n$ find $y'$.

 Challenge Question:  If $y=x^m(bx-c)^n$  where $m,n$ are positive integers, and $b,c$ are non-zero real numbers, show that the first derivative equals

$$y'=\dfrac{dy}{dx}=x^{m-1}(c-bx)^{n-1}\bigg( mc -b(m+n)x\bigg)$$

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

 

Basic differentiation - quick revision

 

Derivative Notation

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Differentiate $y=\dfrac{\sqrt[3]{6-x}}{9}$.

Differentiate $y=x\sqrt{x}$.

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Differentiate $y=x^{10}(1-x)^{12}$

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Differentiation examples

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Differentiation rules

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Tangent and Normal example

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Solve the quadratic inequality $x^2+5x+3 \le 0$