Question

Find the coordinates of the point in the first quadrant at which the tangent line to the curve 7x^3 -xy + y^3 = 0 is parallel to the x-axis.

Answer 1

Am I correct in that I take the derivative first? If so, what's next? Otherwise, what the heck is going on?

Answer 2

for the line to be parallel to x-axis means slope = 0. First cuadrant means x>0 and y>0. So find the derivative, set it to 0, and find the values (>0) for x and y

Answer 3

For the derivative, use implicit derivation:
\(y'=\large-\frac{F_x}{F_y}=-\frac{21x^2-y}{3y^2-x}\)
Now set it equal to 0:
\(\large -\frac{21x^2-y}{3y^2-x}=0\)
which means:
\(y-21x^2=0\)
or
\(y=21x^2\)
remmember that values \(3y^2-x=0\) are not alowed

Answer 4

Excellent, thank you very much