# Finding the equation of a curve

• Mar 11th 2011, 09:26 PM
Ploppies
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.
• Mar 11th 2011, 10:25 PM
earboth
Quote:

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: $\displaystyle y = f(x)=2x^3+x^2+x+4$