– Got it, guys, welcome to our level three

calculus differentiation strategy video. I’m Mackenzie. – And I’m Gabrielle. – And we’re going to

be giving you some tips in getting through the standard. – Cool. So, calculus has so many different kinds of equations, but you can basically say, break them down to three different types. So, the first one is pure equations and so that’s just

differentiating them straight away and that can involve

exponential trigonometry or solving some of the tiniest equations or even finding equations

for a straight line. The second is graphing. And so, that’s noticing points where there might be continuity or where a function might concave

up or down, turning points. And, also where a function is increasing or decreasing. And the third one is application. And so that’s when you’re finding the maximum or minimum of a variable or finding the rate of change

for a variable as well. – So for the standard, you

only need to have three of the questions up to excellence to actually get full marks, which is pretty neato. and we’re going to be,

throughout this video, giving you tips on how to get to there. A key thing to recognize

about the standard is, the examiners like to word things in ways that you often have to re-form it before you can really work with it. So for example, you cannot differentiate this root of a. However, we can turn it into a to the power of a half and a differentiate that so it becomes one over two times the root of a. – So, an important term

to keep yourself familiar with is normal line. And, that’s basically just another way of saying perpendicular line. And this means set at a point

two gradients multiplied by each other are equal to negative one and in equations, you can, it can be worded as a is normal line to the curve or a and b are perpendicular to each other and that’s just talking about the relationship

between the two lines. – Another key skill to bear in mind, especially if you’re

aiming for excellence, is using simultaneous

equations in being able to find the equation for a straight line. A really good place to start with this is by using the general formula for a straight line,

so y equals ax plus c, and filling that in with

information along the way. You don’t want to mix

and match your methods, too much just for the simple

fact that it can get confusing. So find a method that works

for you and really stick to it. – So it’s likely that

you’re going to get a graph which has different types of lines on it and you’ll be asked for different points where the graph is increasing

or decreasing, et cetera And so one thing that is really helpful in that case is if you take the first derivative of that graph, points where the value is positive, as where the graph is

increasing and points where the value is

negative, is decreasing. And then same if you took the second derivative of that graph. So you’ll be able to find where a graph is concave up or concave down. – So we’ve finally come

to the part of the video where we’re answering the

excellence type questions. There are sort of two

main branches of this. The first of which being,

finding the minimum or maximum. So in doing this we can have

an example a question like, you have a piece of paper that’s 50 centimeters by 50 centimeters and they want you to find the maximum regular cube using this paper. So, the first step for

this is to make an equation with your wanted variable on one side and everything else on the other. Secondly, we want to be

making sure everything is in terms of the wanted variable. What this means is that

we only have one like term and so we’re only dealing

with one like unknown variable and everything is in relation to that. Thirdly, we want to differentiate this and make it equal to zero and then there you go. There’s is the excellence

part of your question done. Last optional step for

these kind of questions is popping x back into the equation to a, make sure it’s right and b, look at the second derivatives. Now if it is a negative,

what you’re getting is your maximum value

and if it’s positive, you’re gonna be getting

your minimum value. Use these and compare them to

zero and clearly state this in your answer right at the end. – So the second type

of excellence question that you’ll come across is a rate of change question. So, for example our one

we’re working with today is the volume of the cone changes at a rate of three

centimeters cubed per minute. So what’s the rate of change

for the height of the cone? Now you’re going to break this down into four separate steps. The first thing that you’re

gonna do is write down the differentiated

equation in this question that we already know, so this would be, dv over dt equals three, and so you’re going to also

add in the necessary units and change them if you need to as well, but we don’t need to do that. We can just keep it as

three centimeters cubed. The second thing that you’re gonna do, is write down the equation for the rate of change that you want to find and you can use the equation that we just created there before and change it using the triangle so that’ll equal dh over dt equals dv. over dt times, dt over dh. Now the third thing

that you’re gonna do is, find dt of a dh, using the table, so you can do this by using trigonometry and similar triangles if

that’s useful for you. The fourth thing that you’re going to do is substitute that number in and solve for the final answer and you’re good to go. – So the level three calculus

differentiation standard requires that you’re familiar with a bunch of different kinds of

equations and you need to have the foundational skills to be able to answer them and recognize

them under an exam condition. – Excellence questions are

always going to be the hardest to do as they’re designed to be the most difficult to know where to start, but if you’re using the strategies that we just talked about today, then you should be all good. Also, remembering though,

that it’s really important to study for at least

three of the past exams for that external in order

to get a really good grade. – So we’ve covered the fundamentals of the standard in this video. There’s heaps more in

the walkthrough guides that we have online and you can order a hard copy with next day shipping. And, good luck.