Gradient Function - To discover different curves and their relations, and the formula for the gradient.

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Gradient Function Coursework

Aim

To discover different curves and their relations, and the formula for the gradient.

What is a gradient?

My understanding of a gradient is that it tells us how steep a slope is. The Oxford dictionary says ‘1 a sloping part of a road or railway. 2 the degree of a slope, expressed as change of height divided by distance travelled. 3 Physics a change in the magnitude of a property (e.g. temperature) observed in passing from one point or moment to another.’.

How will I find the gradient?

I will find the gradient by using two methods; the tangent method and the increment method.

The tangent method involves drawing a right angled triangle with the hypotenuse touching the point you want to find the gradient of, and stretching to the two other corners.

See the graph ‘Tangent Method’ .

On this graph we see four letters, D being that of the point and A, B and C being of the triangle. Now to find the gradient with this method we do BC÷AC.

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The increment method, which we use as it is more accurate than the tangent one. You zoom into the graph and take the x point and y point just after a whole figure. For instance with y-x2 , using point (1,1) we would do 1.0012 – 1 for the y value and 1.001 – 1 for the x value. So therefore –

Method = 0.002001 / 0.001 = 2.001, which we can say is roughly 2.

Y=X

Please see graph y=x

As the co-ordinates are the same, the distances between the parts of the ...

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