Integration question help (1 Viewer)

[abdog]

A curve has d^2y/dx^2 = 8x and the tangent at (-2,5) makes an angle of 45 degrees with the x-axis. Find the equation of the curve.

I integrated 8x and got 4x^2 and subbed the x value into it. Where do I go from there? Any hints?

 

[Trebla]

At x = -2, dy/dx = 1 (an angle of 45 degrees to the x-axis has a gradient of 1) and then solve for the constant c. Integrate dy/dx to obtain y and then substitute the point x = -2 and y = 5 to solve for the constant to obtain the specific solution for y.