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

Steps

Step 1 ：Define the function $f (x) = - 6 \cos 3 x + 2$ .

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

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

Step 4 ：Evaluate the function at the critical points and at the endpoints of the interval $[0, π]$ 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 $f (x) = - 6 \cos 3 x + 2$ on the interval $[0, π]$ is $- 4$ and the maximum value is $8$ .

Determine Min and Max from Trig EquationScore: 0/2 Penalty: noneQuestionWatch VideoShow ExampDetermine the minimum and maximum value of the following trigonometric function.f(x)=−6cos⁡3x+2Answer Attempt 1 out of 2Minimum:Maximum:Submit Answer

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Determine Min and Max from Trig Equation
Score: $0 / 2$ Penalty: none
Question
Watch Video
Show Examp
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:
Submit Answer