Determine Min and Max from Trig Equation
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Determine the minimum and maximum value of the following trigonometric function.
\[
f(x)=-6 \cos 3 x+2
\]
Answer Attempt 1 out of 2
Minimum:
Maximum:
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Step 1 ：Define the function \(f(x)=-6 \cos 3x+2\).

Step 2 ：Find the derivative of the function, \(f'(x) = 18\sin(3x)\).

Step 3 ：Set the derivative equal to zero and solve for \(x\) to find the critical points, \(x = \frac{\pi}{6} + k\pi, \frac{5\pi}{6} + k\pi\) where \(k\) is an integer.

Step 4 ：Evaluate the function at the critical points and at the endpoints of the interval \([0, \pi]\) to find the possible maximum and minimum values, \(-4, 8\).

Step 5 ：Compare these values to find the maximum and minimum values of the function on the interval.

Step 6 ：Final Answer: The minimum value of the function \(f(x)=-6 \cos 3x+2\) on the interval \([0, \pi]\) is \(\boxed{-4}\) and the maximum value is \(\boxed{8}\).