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What is the slope of the tangent line of # (3x)/y-(4x^2)/(1-y)^2 =C #, where C is an arbitrary constant, at #(1,2)#?

Answer 1

I am not confident enough to derive a solution but if this is implicit differentiation I can provide you with a solution check point as output from software.
#color(red)("This part solution needs to be checked")#

I should imagine that upon differentiation the constant C would become 0 so you would end up with:

#(x(8xy^2-3y^3+9y^2-9y+3))/(y(8xy^2-3y^3-8xy+9y^2-9y+3))=0#

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Answer 2

Charles Anctil

To find the slope of the tangent line at the point (1,2), first, differentiate the given equation implicitly with respect to x. Then, substitute the coordinates (1,2) into the derivative expression to find the slope of the tangent line. The result will be the slope of the tangent line at the given point.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.