Absolute maxima and minima Determine the location and value of the absolute extreme values of ƒ on the given interval, if they exist.


ƒ(x) = sin 3x on [-π/4,π/3]

Verified step by step guidance

1. Identify the function f(x) = sin(3x) and the closed interval [-π/4, π/3].
2. Calculate the derivative f'(x) to find critical points where f'(x) = 0 or is undefined.
3. Solve the equation f'(x) = 0 to find the critical points within the interval [-π/4, π/3].
4. Evaluate the function f(x) at the critical points found and at the endpoints of the interval, x = -π/4 and x = π/3.
5. Compare the values obtained from the evaluations to determine the absolute maximum and minimum values on the interval.