Asked by Mary
Find the points at which the relation 3x^2-2xy+y^2=24 has a vertical or horizontal tangent line.
Answers
Answered by
drwls
Differentiate both side with respect to x, implicitly.
6x -2y -2x dy/dx +2y dy/dx = 0
dy/dx*(x-y) = 3x -2y
The tangent is vertical at x = y and horizontal at x = 2y/3. Solve the original equation for the corresponding x and y values.
Horizontal tangent at:
3x^2+2x+x^2 = 24
x^2 +x -12 = 0
x = -4 or 3
6x -2y -2x dy/dx +2y dy/dx = 0
dy/dx*(x-y) = 3x -2y
The tangent is vertical at x = y and horizontal at x = 2y/3. Solve the original equation for the corresponding x and y values.
Horizontal tangent at:
3x^2+2x+x^2 = 24
x^2 +x -12 = 0
x = -4 or 3
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