# Thread: Finding the equation of a curve

1. ## Finding the equation of a curve

So I am studying for a maths exam I have tomorrow and came to a question I couldn't figure out.

At any point (x,y) on a curve d^2 y/dx^2 = 12x + 2

Find the Equation of the curve if it passes through (1,8) and the gradient of the tangent at this point is 9.

Thanks for any help.

2. Originally Posted by Ploppies
So I am studying for a maths exam I have tomorrow and came to a question I couldn't figure out.

At any point (x,y) on a curve d^2 y/dx^2 = 12x + 2

Find the Equation of the curve if it passes through (1,8) and the gradient of the tangent at this point is 9.

Thanks for any help.
This is the 2nd derivation of the function y = f(x).

1. $\displaystyle \dfrac{dy}{dx}=\int(12x+2)dx=6x^2+2x+c = f'(x)$

You know that $\displaystyle f'(1)=9$ . Determine c. Thus:

2. $\displaystyle y = \int(6x^2+2x+1)dx=2x^3+x^2+x+d=f(x)$

You know that $\displaystyle f(1)=8$. Determine d.
Spoiler:

3. The function has had the equation: $\displaystyle y = f(x)=2x^3+x^2+x+4$