What does part B even mean?

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It’s a differentiation question. Differentiate x^2 -2x
You get f’(x) = 2x - 2
f’(p) = 2p - 2

It’s because in the first part they’re trying to get you to see the correlation between the x value and the gradient at that point

and then you use that to try figure out what the gradient at p would be

by trying to make equations with the points you do know

so when x = 1 then m = 0

and then at x = -1 you’d draw a tangent and find that m = -6
at x = 2 you’d find that m = 2

and you’d try figure out what is the correlation between these values

Is there an equation which allows me to get from the x value to the gradient

x = -1, m = -6
x = 0, m = -2
x = 1, m = 0
x = 2, m = 2
x = 3, m = 6

since when x=0, m = -2, we can deduce that there is a constant of -2 in our equation
since x = 1, m = 0, we can deduce that the coefficient in front of x is probs 2
so now we have gradient = 2x - 2
Now we check to see if this formula works for all the other values, which it does, and therefore it is our answer