Thread: finding the equation of a curve,

1. finding the equation of a curve,

A curve has gradient function $\displaystyle k(2x-1)^{2}$

and passes through the origin and the point (1,2). Find the equation if the curve.

I am not sure, how would I work out the value of k?

$\displaystyle k \int (2x-1)^{2}$ =

$\displaystyle k \frac{1}{6} (2x-1)^{3} + c$

Is this correct? If so from here, how would I proceed?

I have two unknowns, so unable to put the values of x and y given.

2. A curve has gradient function

and passes through the origin and the point (1,2). Find the equation if the curve.

I am not sure, how would I work out the value of k?

$\displaystyle k \int (2x-2)^2$ = (this is typed wrong ^^!)

$\displaystyle k \frac{1}{6} (2x-1)^{3} + c$

Is this correct? If so from here, how would I proceed?

I have two unknowns, so unable to put the values of x and y given.
It should be $\displaystyle k \frac{1}{6}(2x-1)^3 + C$

There are two points (0,0) and (1,2), so

$\displaystyle \frac{1}{6}k(-1)^3 +C = 0$
and $\displaystyle \frac{1}{6}k(1)^3 + C = 2$

From two above equations, you can solve for k and C

3. Thanks for that, I have edited my mistake.

I get $\displaystyle y = (2x-1)^{3} + 1$