Question

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) =x³ + y³ − 3x² − 9y²− 9x

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = xy + 64/x +64/y

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) =y² − 8ycos(x),    −1 ≤x ≤ 7

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 6 sin(x) sin(y),     −π < x < π,     −π < y < π

Find the absolute maximum and minimum values of f on the set D.

f(x, y) =x² + y² +x²y + 8,

Find the absolute maximum and minimum values of f on the set D.

f(x, y) =x⁴ + y⁴ − 4xy + 7,

D = {(x,y) | 0 ≤ x ≤ 3, 0 ≤y ≤ 2}

absolute maximum value
absolute minimum value

D = {(x,y) | |x| ≤ 1, |y| ≤ 1}

absolute maximum value
absolute minimum value

Answer 1