Calculus
posted by Kenny on .
Could someone please help me with this question;
Find the tangent to the curve y=x^28x+14 which slope is 2. Show that this tangent touches the curve y= x^24x+4. Find the point of contact.
Thank you.

take the derivative of the first equation
y'=2x8
2=2x8
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^28x+14=924+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. 
Thank you Bobpursley.
After doing what you told me, the point of contact I got is, (1,7).
Is this correct?