Term
| How do you find the average speed of a certain amount of time from a distance vs time graph? |
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Definition
| Add the distances, then divide by the amount of time taken to travel that far. |
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Term
| How do you find the speed from a distance/time graph? |
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Definition
| Find the gradient of the (possibly imaginary) line in the area you're looking for |
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Term
| What do speed/time graphs often look like? |
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Definition
| A set of axis with lots of floating platforms |
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Term
| What is rate of change (on a graph) equal to? |
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Definition
| The gradient = change in y values/change in x values = rise/run = the derivative |
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Term
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Definition
| A line that only touches the curve of a function in one place |
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Term
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Definition
| A line that cuts the curve of a function in two places |
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Term
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Definition
| The limit of a function (at a certain point on the line) is the expected value of the function at that point (if it exists). |
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Term
| A limit will only exist when... |
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Definition
| ... the expected value is the same coming from both sides on the line of the function. |
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Term
| What does limit notation look like? |
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Definition
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Term
How would you solve the following?
lim (x^2 -3x +5) = ?
x -> 2 |
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Definition
Sub in 2 wherever x was.
(2)^2 - 3(2) + 5
= 4 - 6 + 5
= 3 |
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Term
How would you solve the following?
lim (x^2 - 9)/(x - 3) = ?
x -> 3 |
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Definition
Factorise, cancel and then sub in 3 wherever x was.
lim [(x+3)(x-3)]/(x-3)
x -> 3
= lim (x + 3)
x -> 3
= 3 + 3
= 6 |
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Term
| What is the process of finding the derivative called? |
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Definition
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Term
What is the notation of the following when it is made into a derivative:
f(x)
y |
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Definition
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Term
Differentiate:
3x^3 - 4x^2 + 5x - 7 |
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Definition
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Term
| Which four main things must be labelled and drawn when graphing functions? |
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Definition
| The x and y intercept(s), the turning point(s), write the equation on the graph and draw the line of the function. |
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Term
What kinds of stationary points do the following things represent?
+ 0 -
- 0 +
+ 0 +
- 0 - |
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Definition
+ 0 - ... relative maximum
- 0 + ... relative minimum
+ 0 + ... point of inflection rising
- 0 - ... point of inflection falling |
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