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 March 1st, 2009, 11:01 AM #1 Newbie   Joined: Mar 2009 Posts: 6 Thanks: 0 Find eqation of tangent line Im stuck on a few... y = 5?x^3 ; when x = 0 ( 5th root, in case it doesn't turn out) and p(x) = ax^2 + bx + c ; x = -b/2a ; a, b, and c are constants, a not = 0
 March 1st, 2009, 12:42 PM #2 Senior Member   Joined: May 2008 From: Sacramento, California Posts: 299 Thanks: 0 Re: Find eqation of tangent line $y'=\frac{3}{5x^{2/5}}$ (power rule), so at $x=0$, $y'=-\infty$. $p'(x)=2ax+b$ (power rule again), so at $x=\frac{-b}{2a}$, $p'(x)=0$. This would make sense because the function's vertex is at $x=\frac{-b}{2a}$. To get the equation of the tangent line, use point-slope ($f(x)=m(x-x_1)+y_1$); plug in the slope of the curve at the point for $m$ and the coordinates of the point for $x_1$ and $y_1$. For $y$, the line is undefined, but for $p(x)$, the equation would be $f(x)=\frac{-b^2}{4a}+c$.
 March 1st, 2009, 12:54 PM #3 Newbie   Joined: Mar 2009 Posts: 6 Thanks: 0 Re: Find eqation of tangent line Thanks sidT, helped a lot!

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