Could someone please help me with this question;

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.

Answer 1

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.

Answer 2

Thank you Bobpursley.

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

Is this correct?