Calculate the directional derivative of f at the point 30

Question

1. Let f(x, y) = x² + e^xy.

a. Calculate the directional derivative of f at the point (3.0) in the direction (2, -3).

b. What is the maximum directional derivative of f and in what direction does this occur?

2. Let R be the region in R² bounded by the circle x² + y² = 4 and let f(x, y) = x² + y² - 2y + 3. Find the minimum and maximum values of f(x, y) on R.