1. ## find f(x) dy/dx

The graph of $y = f(x)$ passes through the point $(1,2)$ and has a horizontal tangent at that point.

If $\frac{d^2y}{dx^2} = 4x - 5$ find f(x) exactly.

I have absolutely no idea on how to even approach this question

Thank you to anyone who attempts : )

2. Originally Posted by qzno
The graph of $y = f(x)$ passes through the point $(1,2)$ and has a horizontal tangent at that point.

If $\frac{d^2y}{dx^2} = 4x - 5$ find f(x) exactly.

I have absolutely no idea on how to even approach this question

Thank you to anyone who attempts : )
Integrate once and set $y' = 0, x = 1$ to find your first constant of integration, then integrate again and use the fact that (1,2) is on the curve to find the second constant of integration.

3. what do you mean by integrate and constants of integration?

4. so i take the antiderivative of $4x -5$ and i get $2x^2 - 5x + c$ and then i use the info given to solve for c?

5. That's it. You have the conditions $y(1) =2$and $y'(1)=0$ Don't forget to derive twice (two constants)