Using a table to suggest a rule for a gradient.
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Using a table to suggest a rule for a gradient.

[From: ] [author: ] [Date: 12-06-25] [Hit: ]
3,4, 5,.........
My text book says to "suggest a rule for determining the gradient of y =x^2 at some point (a,a^2)".
So I've managed to create a table for Y = x^2, as shown below:

X: 0,1,2,3,4, 5,...
gradient: 0,2,4,6,8,10...

But how am I meant to explain this in the form (a,a^2)?
I know that the gradient is equal to 2 times X, would that be a suitable rule suggestion for the question?

-
The question does not indicate how you are to find the gradient. You are correct, it is 2 times X.
The (a,a^2) are coordinates of the point on the curve where x=a so that y=a^2, which
gives gradient=2 times a or 2a.
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