Use the formula obtained in Exercise 84 to find the slope of the level curve x²y + 2y³ − 2e^−x = 14 at the point (0, 2). What is the equation of the tangent line to the level curve at this point?

Data from Exercises 84

Suppose y = h(x) is a differentiable function of x and that F(x, y) = C for some constant C. Use the chain rule (with x taking the role of t) to show that

Conclude that the slope at each point (x, y) on the level curve F(x, y) = C is given by

Transcribed Image Text:

ƏF Əx + JF dy dy dx = 0