Differentiation Revision Notes for Core 2

Some notes that I created for differentiation for Core 2.

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  • Created by: George
  • Created on: 12-05-11 21:53
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Mathematics ­ Core 2 Differentiation
Increasing and Decreasing functions
Increasing functions are functions that have a gradient greater than 0.
So dy / dx > 0.
You can work if a function is an increasing function if you differentiate the term and then see if
at the point you are considering the gradient is greater than 0.
For example:
If we need to show that the function of x 2 is an increasing function at 2.
dy / dx = 2x
2 x 2 = 4 of which is greater than 0, so it is an increasing function.
Decreasing function are functions that have a gradient less than 0.
So dy / dx < 0.
You can work if a function is a decreasing function if you differentiate the term and then see if
at the point you are considering has a gradient is less than 0.
For example:
If we need to show that the function of x 2 is an increasing function at 2.
dy / dx = 2x
2 x 2 = 4 of which is less than 0, so it is a decreasing function.
Summary
dy / dx > 0 is an increasing function
dy / dx < 0 is a decreasing function
dy / dx = 0 is a stationary point or turning point

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Stationary Points
Stationary points are points on the curve where the gradient is equal to 0. They can also be
called turning points. You can work them out by just letting the differentiated term equal 0.
For example:
If we need to work out where the coordinate of the stationary point on an x 2 curve we
differentiate and then let it equal 0.…read more

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When x = 1, d 2 y / dx 2 = 18 < 0, so it is maximum point. (1, 17) is a maximum point.
When x = 4, d 2 y / dx 2 = 18 > 0, so it is a minimum points. (4, 10) is a minimum point.…read more

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S = 280 cm2…read more

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