hi all pls all

Find the value of c such that y = x + c is a tangent to the parabola y = X^2 -x - 12

please solve the entire equation with explanation please. ty.

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- Feb 23rd 2008, 02:05 AMandrew2322tangent of a parabola
hi all pls all

Find the value of c such that y = x + c is a tangent to the parabola y = X^2 -x - 12

please solve the entire equation with explanation please. ty. - Feb 23rd 2008, 04:29 AMPlato
- Feb 23rd 2008, 08:31 AMTheEmptySet
$\displaystyle \frac{dy}{dx}=2x-1$

Since the line is written in slop intercept form

$\displaystyle y=x+c$ we know that the slope of line is

$\displaystyle m=1$

Since we need the slope to equal the derivative we get...

$\displaystyle 1=2x-1$ solving for x we get

$\displaystyle x=1$ This gives us half of the ordered pair...

plugging this into the equation of the parabola we get

$\displaystyle y=(1)^2-(1)-12=-12$ This completes our ordered pair giving us (1,-12)

Now finally we use this ordered pair to solve for c plugging the ordered pair into the equation of the line we get....

$\displaystyle -12=1+C$ solving for C we finally end up with...

$\displaystyle y=x-13$

I hope this helps. Remember that the derivative represents the slope of the graph at any point.(Rock)