Posted by **Kenny** on Monday, February 22, 2010 at 9:12pm.

Could someone please help me with this question;

Find the tangent to the curve y=x^2-8x+14 which slope is -2. Show that this tangent touches the curve y= -x^2-4x+4. Find the point of contact.

Thank you.

- Calculus -
**bobpursley**, Monday, February 22, 2010 at 9:18pm
take the derivative of the first equation

y'=2x-8

-2=2x-8

x= 3 is where the tangent has the slope of -2

so the equation of that tangent line is

y=-2x+b to find b, you have to find y at x=3

y= x^2-8x+14=9-24+14

now put that y into

y=-2x + b and solve for b.

Now you have the line. I will leave it up to you to show this line is tangent to the second curve, the process is very similar.

- Calculus -
**Kenny**, Monday, February 22, 2010 at 10:31pm
Thank you Bobpursley.

After doing what you told me, the point of contact I got is, (-1,7).

Is this correct?

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