Find the critical points of the following functions on the given intervals. Identify the absolute maximum and absolute minimum values (if they exist).
ƒ(x) = sin 2x + 3 on [-π , π]

Verified step by step guidance

1. First, find the derivative of the function ƒ(x) = sin(2x) + 3. This will help us identify the critical points where the slope of the function is zero or undefined.
2. Set the derivative equal to zero and solve for x. This will give you the critical points within the interval [-π, π].
3. Evaluate the function ƒ(x) at the critical points found in the previous step, as well as at the endpoints of the interval, which are x = -π and x = π.
4. Compare the values of ƒ(x) obtained from the critical points and the endpoints to determine the absolute maximum and minimum values on the interval.
5. Conclude by stating the absolute maximum and minimum values along with their corresponding x-values.