Questions from General Calculus

Q: A pentagon is formed by placing an isosceles triangle on a rectangle

A pentagon is formed by placing an isosceles triangle on a rectangle, as shown in the figure. If the pentagon has fixed perimeter P, find the lengths of the sides of the pentagon that maximize the are...

Q: Find the local maximum and minimum values and saddle points of the

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the importa...

Q: Find the local maximum and minimum values and saddle points of the

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the importa...

Q: Use a graph or level curves or both to estimate the local

Use a graph or level curves or both to estimate the local maximum and minimum values and saddle points of f (x, y) = x3 - 3x + y4 - 2y2. Then use calculus to find these values precisely.

Q: Use a graphing calculator or computer (or Newton’s method or a

Use a graphing calculator or computer (or Newton’s method or a computer algebra system) to find the critical points of f (x, y) = 12 + 10y - 2x2 - 8xy - y4 correct to three decimal places. Then classi...

Q: Use Lagrange multipliers to find the maximum and minimum values of f

Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint(s).

Q: Sketch the graph of the function. f (x,

Sketch the graph of the function. f (x, y) = x2 + (y – 2)2

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. 5. If f is continuous on [0, 1], then...

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. 1. 2. There exists a function f with contin...

Q: Plot the point whose cylindrical coordinates are given. Then find the

Plot the point whose cylindrical coordinates are given. Then find the rectangular coordinates of the point. (a). (4, π/3, -2) (b). (2, - π/2, 1)