# Differentiation by first principles *help please*

The question is

A curve has equation y = x^3 - x^2
Find the gradient of the line passing through the point (5,100) and the point on the curve for which x = 5 + h

My thoughts were f(5+h) = (5+h)^3 - (5+h)^2 so therefore f(x) = (5)^3 - (5)^2 then to sub into the first principles formula but idk if the f(x) part I am doing correctly? Then sub in the 5 into the answer

Can someone help? Thanks!
(edited 3 months ago)
Original post by Kittycatellie123
The question is

A curve has equation y = x^3 - x^2
Find the gradient of the line passing through the point (5,100) and the point on the curve for which x = 5 + h

My thoughts were f(5+h) = (5+h)^3 - (5+h)^2 so therefore f(x) = (5)^3 - (5)^2 then to sub into the first principles formula but idk if the f(x) part I am doing correctly?

Can someone help? Thanks!

You want a line passing through the two points
(5,100)
and
(5+h, (5+h)^3-(5+h)^2)
so ...
Original post by mqb2766
You want a line passing through the two points
(5,100)
and
(5+h, (5+h)^3-(5+h)^2)
so ...

Thanks I got h^2 + 14 h + 65
Original post by Kittycatellie123
Thanks I got h^2 + 14 h + 65

Not worked it though, but looks about right.