calculus
posted by Fareha .
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 with slope equal to the slope at (2, 1)

calculus 
Fareha
sorry here's the equation:
x+xy+2y^2=6 
calculus 
MathMate
x+xy+2y^2=6
(a)
x(1+y)=62y²
x=(62y²)/(1+y)
differentiate with respect to y to get
dx/dy=4x/(x+1)(62x^2)/(x+1)^2
So
dy/dx
= 1/(dx/dy)
= (1/2)(x^2+2x+1)/(x^2+2x+3)
(b) For the point (2,1), first check that it lies on the curve.
f'(2)=(1/2)(2^2+2*2+1)/(2^2+2*2+3)
=9/22
(c)
Now solve for
f'(x)=9/22
to get x=4 or x=2
Verify all the numerical values. 
calculus  correction 
MathMate
There was a mistake in the calculation of dx/dy. It should have been expressed in terms of y and not x.
Given : x+xy+2y^2=6
(a)
x(1+y)=62y²
x=(62y²)/(1+y)
differentiate with respect to y to get
dx/dy=4y/(y+1)(62y^2)/(y+1)^2
So
f'(y)=dy/dx
= 1/(dx/dy)
= (1/2)(y^2+2y+1)/(y^2+2y+3)
(b) For the point (2,1), first check that it lies on the curve.
f'(y)=
f'(1)=(1/2)(1^2+2*1+1)/(1^2+2*1+3)
=1/3
Tangent line with slope 1/3 passing through (2,1) is:
(y1) = (1/3)(x2)
(c)
Now solve for
f'(y)=1/3
to get x=3 or x=1
Please verify all the numerical values.
Respond to this Question
Similar Questions

Help Calc.!
original curve: 2y^3+6(x^2)y12x^2+6y=1 dy/dx=(4x2xy)/(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 … 
last calc question, i promise!
given the curve x + xy + 2y^2 = 6... a. find an expression for the slope of the curve. i got (1y)/(x + 4y) as my answer. b. write an equation for the line tangent to the curve at the point (2,1). i got y = (1/3)x + (5/3). but i … 
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 y5 = 1/18 (x3) ] b.) What is the smallest slope on the curve? 
calculus
Consider the curve given by the equation y^3+3x^2y+13=0 a.find dy/dx b. Write an equation for the line tangent to the curve at the point (2,1) c. Find the minimum ycoordinate of any point on the curve. the work for these would be … 
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 … 
Calculus
Please help this is due tomorrow and I don't know how to Ive missed a lot of school sick Consider the curve given by the equation x^3+3xy^2+y^3=1 a.Find dy/dx b. Write an equation for the tangent line to the curve when x = 0. c. Write … 
Calculus
The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve? 
Calculus
The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve? 
Calculus AB
Could someone please help me with these tangent line problems? 
Calculus
The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (2, 1) is a point on the curve?