Question

Given equation y2 = x3 - 2x + 5 (I found derivative: dy/dx = (3x2 - 2)/(2y)) a. determine algebraically what u coordinates on the curve tangent line is horizontal b. determine algebraically what x coordinates on this curve tangent line is vertical

Answer 1

a. 1.If the line is horizontal, then you know that the slope = 0, so just set the derivative equal to zero, and solve.
b. If the tangent line is vertical, then the slope doesn't exist. So you can just set the denominator of the derivative equal to zero.

Answer 2

horizontal whenever 3x^2-2=0 and vertical whenever 2y=0

Answer 3

yeah I understand that part but I don't understand the algebra of what do afterwards. cuz then you get x = 2/3^1/2 and y = 0. what next?

Answer 4

Then substitute back into the original equation and solve for the other variable.