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.
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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):Quote:
Originally Posted by vixity
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?
Yes and thanks