Find the Equation of a Tangent Line using Implicit Diff.

What is an implicit function?

• "y = some function of x". When we know x can calculate y directly.
• "x = some function of y". When we know y can calculate x directly.
• "some function of x and a constant equal to y".
• "some function of y and x equal something else". Knowing x does not lead directly to y.

Find the equation of the tangent line of the function:
x³ - 7xy + y³ = -125 at (2,1)

• y - 1 = 0.45 (x - 2)
• y - 1 = -0.45 (x - 2)
• y - 1 = 2.2 (x - 2)
• y - 1 = -2.2 (x - 2)

• y - 8 = 0.2321 (x - 1)
• y - 8 = -0.2321 (x - 1)
• y - 8 = 4.308 (x - 1)
• y - 8 = -4.308 (x - 1)

Find the equation of the tangent line of the function:
(y - 5)⁵ = x² + 2xy - 33 at (-3, -1)

• y + 1 = -0.006 (x + 3)
• y - 1 = -0.006 (x - 3)
• y + 1 = 160.75 (x + 3)
• y - 1 = 160.75 (x - 3)

• y - 1 = 0.6 (x - 1)
• y - 1 = -0.6 (x - 1)
• y - 1 = 1.67 (x - 1)
• y - 1 = -1.67 (x - 1)

• y - 2 = 0.93 (x - 3)
• y - 2 = -15/14 (x - 3)
• y - 2 = 15/14 (x - 3)
• y - 2 = -0.93 (x - 3)