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[SOLVED] Calculus - Derivative Help??
Consider the curve given by the equation y^3 + 3x^(2)y + 13 = 0. Find the minimum y - coordinate of any point on the curve. Justify your answer.
I solved parts a&b:
dy/dx = -6xy / (3y^2 + 3x^2)
Equation for line tangent to curve at (2,-1): y + 1 = 4/5 (x-2)
This is the other problem I cannot get. I tried to make up my own minimum to find a relative minimum, which my instructor said we could find, but I still couldn't get critical points. I also tried using the second derivative ... but that got too messy and I didn't know what to do.
Any help would be fantastic! Thank you for your time and explanations!
Homework Statement
Consider the curve given by the equation y^3 + 3x^(2)y + 13 = 0. Find the minimum y - coordinate of any point on the curve. Justify your answer.
Homework Equations
I solved parts a&b:
dy/dx = -6xy / (3y^2 + 3x^2)
Equation for line tangent to curve at (2,-1): y + 1 = 4/5 (x-2)
The Attempt at a Solution
This is the other problem I cannot get. I tried to make up my own minimum to find a relative minimum, which my instructor said we could find, but I still couldn't get critical points. I also tried using the second derivative ... but that got too messy and I didn't know what to do.
Any help would be fantastic! Thank you for your time and explanations!