math
posted by rita .
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....

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)
Respond to this Question
Similar Questions

Please check my maths?
How should i do this question?? it says: find the equation of the tangent to the curve y=(x2)^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 part, 
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. 
math
find the eqt. of tangent to the curve y=x^2+2x10 @ the point where the curve cuts the yaxis.[ans:y=2x10] how do i do this because they didn't give me the point...? 
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 … 
calculus
Consider the curve defined by 2y^3+6X^2(y) 12x^2 +6y=1 . a. Show that dy/dx= (4x2xy)/(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 … 
Math
a curve is such that dy/dx=4x+7. the line y=2x meets the curve at point 'P'. Given that the gradient of the curve at P is 5. State the coordinates of P. 
Math
a curve is such that dy/dx=4x+7. the line y=2x meets the curve at point 'P'. Given that the gradient of the curve at P is 5. State the coordinates of P. 
Parabola ques
the normal to a parabola y^2=4ax at the point t,where t is not 0 meets the curve again at the point t'.find t' in terms of t.determine a point on the xaxis where the tangent at t' meets the xaxis. 
Calculus AB
Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x1)e^x. For which value of x is the slope of the tangent line to f positive? 
Calculus AB
Could someone please help me with these tangent line problems?