Calculus

posted by .

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?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. please help; calc

    original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point …
  2. calculus

    Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2 + 1 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent …
  3. 12th Grade Calculus

    1. a.) Find an equation for the line perpendicular to the tangent curve y=x^3 - 9x + 5 at the point (3,5) [* for a. the answer that I obtained was y-5 = -1/18 (x-3) ] b.) What is the smallest slope on the curve?
  4. calculus

    1. Given the curve a. Find an expression for the slope of the curve at any point (x, y) on the curve. b. Write an equation for the line tangent to the curve at the point (2, 1) c. Find the coordinates of all other points on this curve …
  5. calculus

    Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope -1 is tangent to the curve …
  6. Calculus

    Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2y-x) (b) Find all points (x,y) on the curve where the line tangent to the curve has slope 1/2. (c) Show that there are now points (x,y) on the curve where the line tangent …
  7. Calc AB

    Suppose that f(x) is an invertible function (that is, has an inverse function), and that the slope of the tangent line to the curve y = f(x) at the point (2, –4) is –0.2. Then: (Points : 1) A) The slope of the tangent line to the …
  8. mathematics-slope of tangent

    Find the slope of the tangent to the curve x^2+xy+y^2=4 at the point(2,-2) please show workings #thanks
  9. Calculus AB

    Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive?
  10. Calculus AB

    Could someone please help me with these tangent line problems?

More Similar Questions