GCSE Maths Coursework on Gradient Function

what about gradient function. need more detail.

i did one on gradient function where i had to use differentiation. If its the same one i can help.

You can approximate the gradient by drawing a tangent.

But you will get a more accurate answer if you use a calculator in the following way.

Say you want to know the gradient of the curve y = x^5 (ie, y = x raised to the power 5) when x = 3.

That gradient is approximately

[(3 + very small number)^5 - 3^5] / (very small number)

The "very small number" has to be the same in both places.

For example, you could calculate

(3.00001^5 - 3^5)/(0.00001) = 405.003

Thanks for that! At the moment I am drawing the graphs for y=x2, y=x3, y=2x2, y=x3, etc and then finding the gradient from them by drawing a tangent to the curve. What I don't understand is how to find the pattern, which is what we are supposed to do now.

The pattern for y = x^2 is easy to spot - if you're good at drawing tangents (or use the calculator method).

x | gradient of curve at x
-------------------------
0 | 0
1 | 2
2 | 4
3 | 6
4 | 8
5 | 10

Have you found the pattern for y = x^3 ?