Posted by anonymous on Monday, January 28, 2008 at 6:38pm.
x^2x^2y=y^21
find all points on the curve where x=2. Show there is a horizontal tangent to the curve at one of the points.

calculus  Reiny, Monday, January 28, 2008 at 9:02pm
sub x = 2 into your equation to get
4  4y = y^2  1
0 = y^2 + 4y  5
(y+5)(y1) = 0
so when x=2, y =5 or when x=2, y = 1
so the points are (2,5) and (2,1)
check them by subbing them back into the original equation, they work

calculus  Reiny, Monday, January 28, 2008 at 9:38pm
I found the derivative of your equation implicitly and got
dy/dx = (2x+2xy)/(2y = x^2)
for a horizontal tangent this has to be zero, which means the numerator should be zero
subbing in (2,5) makes the top zero, so there is a horizontal tangent at the point (2,_5)
Answer This Question
Related Questions
 Calculus  Consider the curve y^2+xy+x^2=15. What is dy/dx? Find the two points ...
 calculus  dy/dx= (2x2xy)/(x^2+2y) find all points on the curve where x=2. show...
 calculus  dy/dx= (2x2xy)/(x^2+2y) Find all points on the curve where x=2. Show...
 calculus  dy/dx= (2x2xy)/(x^2+2y) Find all points on the curve where x=2. Show...
 Calculus  Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2yx...
 Calculus AB  Could someone please help me with these tangent line problems? 1) ...
 Calculus  Can someone show how this question is solved. Consider the curve ...
 calculus  Given the curve defined by the equation y=cos^2(x) + sqrt(2)* sin(x) ...
 Calculus  Please help this is due tomorrow and I don't know how to Ive missed a...
 Calculus  a)The curve with equation: 2y^3 + y^2  y^5 = x^4  2x^3 + x^2 has ...
More Related Questions