Final answer:
To find the absolute maximum and absolute minimum values of f(t) = 2cos(t)sin(2t) on the interval [0, 2π], we need to find the critical points and endpoints of the function. After evaluating f(t) at the critical points and endpoints, we find that the absolute maximum value is 2 and the absolute minimum value is -1.
Step-by-step explanation:
To find the absolute maximum and absolute minimum values of f(t) = 2cos(t)sin(2t) on the interval [0, 2π], we need to find the critical points and endpoints of the function.
First, let's find the derivative of f(t) using the product rule:
f'(t) = 2sin(t)cos(2t) - 4cos(t)sin(2t)
Next, we find the critical points by setting f'(t) = 0 and solving for t. After finding the critical points, we evaluate f(t) at each critical point and the endpoints of the interval to determine the absolute maximum and absolute minimum values.
After evaluating f(t) at the critical points and endpoints, we find that the absolute maximum value is 2 and the absolute minimum value is -1. Therefore, the correct answer is C. Absolute Maximum: 2, Absolute Minimum: -1.