Show, by differentiating the equation, that if the tangent line at a point (x, y) on the curve x 2 y 2x 8y 2 is horizontal, then xy 1 Then substitute y x 1 in x 2 y 2x 8y 2 to show that the tangent line is horizontal at the points (2, 1 2) and ( 4, 1 4) ...

Taking the derivative on both sides of the equation xy 2x 8y 2 yields 21 xy x 8 xy ...

Show, by differentiating the equation, that if the tangent line at a point (x, y) on the

Question:

Show, by differentiating the equation, that if the tangent line at a point (x, y) on the curve x²y − 2x + 8y = 2 is horizontal, then xy = 1. Then substitute y = x⁻¹in x²y − 2x + 8y = 2 to show that the tangent line is horizontal at the points (2, 1/2) and (− 4, −1/4).

Fantastic news! We've Found the answer you've been seeking!