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Calculus

posted by on .

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 - ,

    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 - ,

    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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