find f(x) dy/dx

Printable View

January 11th 2009, 03:23 PM
qzno

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 : )
January 11th 2009, 03:25 PM
Danny

Quote:

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.
January 11th 2009, 03:31 PM
qzno

what do you mean by integrate and constants of integration?
January 11th 2009, 03:42 PM
qzno

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?
January 11th 2009, 04:02 PM
vincisonfire

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

All times are GMT -8. The time now is 08:56 PM.