1. Find the value forcfor which y=x+cis a tangent to y=3-x-5x^2

don't understand what to do :(

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- Oct 31st 2007, 08:16 AMlra11equation-geometrical
1. Find the value for

*c*for which y=*x+c*is a tangent to y=3-x-5x^2

don't understand what to do :( - Oct 31st 2007, 08:32 AMKrizalid
You gotta find first the intersection of the line and the curve, so

$\displaystyle x+c=3-x-5x^2\implies5x^2+2x+(c-3)=0.$

Now, so that the line be tangent to the curve, the discriminant of the previous equation must be zero, so $\displaystyle 4-4\cdot5(c-3)=0\implies1-5(c-3)=0.$

Solvin' for $\displaystyle c$ yields the desired answer. - Oct 31st 2007, 08:32 AMred_dog
The system formed by the two equations must have an unique solution.

Plug y from the first equation in the second and you'll obtain a quadratic equation. Put the condition that $\displaystyle \triangle =0$, where $\displaystyle \triangle =b^2-4ac$ (a,b,c are the coefficients of the quadratic equation).