Questions from General Calculus

Q: Let f (x, y, λ) = xy +

Let f (x, y, λ) = xy + λ(5 - x - y). Find ∂f/∂x, ∂f/∂y and ∂f/∂λ.

Q: Let f (x, y) = x3y + 8.

Let f (x, y) = x3y + 8. Compute ∂f/∂x (1, 2) and ∂f/∂y (1, 2).

Q: Let f (x, y, z) = (x

Let f (x, y, z) = (x + y) z. Evaluate ∂f/∂y at (x, y, z) = (2, 3, 4).

Q: Let f (x, y) = x5 - 2 x3y

Let f (x, y) = x5 - 2 x3y + ½ y4. Find ∂2f/∂x2, ∂2f/∂y2, ∂2f/∂x∂y, and ∂2f/∂y∂x.

Q: Let f (x, y) = 2x3 + x2y -

Let f (x, y) = 2x3 + x2y - y2. Compute ∂2f/∂x2, ∂2f/∂y2 and ∂2f/∂x∂y (x, y) = (1, 2).

Q: A dealer in a certain brand of electronic calculator finds that (

A dealer in a certain brand of electronic calculator finds that (within certain limits) the number of calculators she can sell per week is given by f (p, t) = - p + 6t - .02 pt, where p is the price o...

Q: The crime rate in a certain city can be approximated by a

The crime rate in a certain city can be approximated by a function f (x, y, z), where x is the unemployment rate, y is the number of social services available, and z is the size of the police force. E...

Q: Find all points (x, y) where f (x

Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = -x2 + 2y2 + 6x - 8y + 5

Q: Find all points (x, y) where f (x

Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = x2 + 3xy - y2 - x - 8y + 4

Q: Suppose that a topographic map is viewed as the graph of a

Suppose that a topographic map is viewed as the graph of a certain function f (x, y). What are the level curves?