calculus prob

[vixity]

Given the gradient function of a curve is x(squared) - 4x + 1 and that the curve passes through the point (-1,2), find the equation of the curve.

[Dross]

Given the gradient function of a curve is x(squared) - 4x + 1 and that the curve passes through the point (-1,2), find the equation of the curve.

The first part of the problem tells you that (letting f(x) be the function of the curve):

f'(x) = x² - 4x + 1

Intigrate this with respect to x and you'll get the function of the curve itself, f(x), with a constant of intigration at the end.

Now you can use the fact that the curve passes through the point (-1,2) - this means that when x = -1, f(x) = 2. Substitute these values into the formula for f(x) that you have and you'll be able to find the constant of intigration, giving you the formula for f(x).

Is this clear?

[vixity]

Yes and thanks