math

find the coordinates of the point where the tangent to the curve y=x^3 +x +2 at the point (1,4) meets the curve again. [ans:-2,-8]
pls help me i don't understand the question....

  1. 👍 0
  2. 👎 0
  3. 👁 50
asked by rita
  1. dy/dx = 3x^2 + 1
    at (1,4) , dy/dx = 4
    tangent equation
    4 = 4(1) + b
    b = 0
    the tangent equation at (1,4) is y = 4x
    where does this cross or touch y = x^3 + x + 2 ?
    x^3 + x + 2 = 4x
    x^3 - 3x + 2 = 0
    let f(x) = x^3 - 3x + 2
    f(1) = 1 - 3 + 2 = 0 , so x-1) is a factor

    by synthetic division ...
    x^3 - 3x + 2 = (x-1)(x^2 + x - 2)
    = (x-1)(x-1)(x+2)

    then the roots of x^3 - 3x + 2 = 0 are
    x = 1 and x = -1 and x = -2
    we knew x = 1 from the tangent part, so the new x = -2 is the other intersection point value
    if x = -2
    y = -8 - 2 + 2 = -8

    the other point is (-2,-8)

    1. 👍 0
    2. 👎 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

    asked by Taeyeon on February 26, 2012
  2. Please check my maths?

    How should i do this question?? it says: find the equation of the tangent to the curve y=(x-2)^3 at the point (3,1). calculate the coordinates of the point where this tangent meets the curve again. I know how to get the first

    asked by holly on June 19, 2009
  3. math

    the tangent yo the curve y=x^2 +5x -2 @ the point (1,4)intersect the normal to the same curve @ the point (-3,-8) at the point P.Find the coordinates of point P.[ans: -1/3,-16/3] just give me some hint to calculate this solution.

    asked by rob on July 22, 2011
  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

    asked by Fareha on December 3, 2011
  5. Maths

    Point P in the curve y=x^3 has coordinates (3,27) and PQ is the tangent to the curve at P.Point Q touches the x-axis.Find the area of the region enclosed between the curve, PQ and the x-axis. My answer: I used differenttiation to

    asked by Debora on March 12, 2017
  6. Calculus AB

    Could someone please help me with these tangent line problems? 1) Find the equation of the line tangent to the given curve at the indicated point: 3y^3 + 2x^2 = 5 at a point in the first quadrant where y=1. 2) Show that there is

    asked by Annie on November 25, 2016
  7. Calculus - Maths

    I got a few questions. Hope ya'll can help out. 1) for F(X) = 6x - 2x^2 Find the gradient of the chord joining the point where the X coorinates are 1 and (1+h) respectively. b) hence find the gradient at x=1 2) Find the

    asked by xxCeLoL on November 26, 2007
  8. Calculas-Differentiation

    Find the coordinates of a point on the curve y=6-x^2 at which the tangent of the curve at the point is perpendicular to the line y=1/4x+1.

    asked by Lam on November 8, 2016
  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? Negative? Zero? 2) Find an equation of the tangent line to the oven curve

    asked by Annie on October 30, 2016
  10. Calculus

    Consider the curve y^2+xy+x^2=15. What is dy/dx? Find the two points on the curve where y equals 0 and show that the tangent lines there are parallel. Find the coordinates of all points on the curve where there is a horizontal

    asked by K.Jeanes on April 19, 2011

More Similar Questions