Find the maximum and minimum values attained by the function f along the path c(t). (a) f(x, y) = xy; c(t) = (cos(t), sin(t)); 0 ≤ t ≤ 2π maximum value minimum value (b) f(x, y) = x2 + y2; c(t) = (cos(t), 4 sin(t)); 0 ≤ t ≤ 2π maximum value minimum value

a) Therefore, the minimum value of the function f is -1/2.

Therefore, the maximum value of the function f is 1/2.

b)Therefore, the minimum value of the function f is 1.

Therefore, the maximum value of the function f is 16.

Step-by-step explanation:

We find the maximum and minimum values attained by the function f along the path c(t). From exercise we have:

a)

Therefore, we get:

We know that:

Therefore, the minimum value of the function f is -1/2.

Therefore, the maximum value of the function f is 1/2.

We use software to drawn a graph.

b)

Therefore, we get:

We know that:

Therefore, the minimum value of the function f is 1.

Therefore, the maximum value of the function f is 16.

We use software to drawn a graph.

Check the attached

Step-by-step explanation:

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step-by-step explanation: