Problem 56E

56. (a) Use implicit differentiation to find $y^{\prime}$ if

$$ x^{2}+x y+y^{2}+1=0 $$

(b) Plot the curve in part (a). What do you see? Prove that what you see is correct.

(c) In view of part (b), what can you say about the expression for $y^{\prime}$ that you found in part (a)?

Step-by-Step Solution