Posted by rita on Friday, July 22, 2011 at 9:34am.
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....

math  Reiny, Friday, July 22, 2011 at 10:45am
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 x1) is a factor
by synthetic division ...
x^3  3x + 2 = (x1)(x^2 + x  2)
= (x1)(x1)(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)
Answer This Question
Related Questions
 Please check my maths?  How should i do this question?? it says: find the ...
 math  the tangent yo the curve y=x^2 +5x 2 @ the point (1,4)intersect the ...
 calculus  1. Given the curve a. Find an expression for the slope of the curve ...
 Calculus AB  Sorry but I've got a lot of problems that I don't understand. 1) ...
 calculus  Consider the curve defined by 2y^3+6X^2(y) 12x^2 +6y=1 . a. Show ...
 Math  a curve is such that dy/dx=4x+7. the line y=2x meets the curve at point '...
 Math  a curve is such that dy/dx=4x+7. the line y=2x meets the curve at point '...
 math  find the eqt. of tangent to the curve y=x^2+2x10 @ the point where the ...
 Parabola ques  the normal to a parabola y^2=4ax at the point t,where t is not 0...
 Calculus AB  Could someone please help me with these tangent line problems? 1) ...
More Related Questions