26. Let $$ f(x)=-3 \cos x+3 $$ The maximum value attained by $$ f $$ on the closed internal $$ [0,2 \pi] $$ oecurs when $$ x $$ is equal to $$ \begin{array}{llll} ext { A. }-3 & ext { B. } 0 & ext { C. } \frac{\pi}{2} & ext { D, } \%\end{array} $$

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26. Let $$ f(x)=-3 \cos x+3 $$ The maximum value attained by $$ f $$ on the closed internal $$ [0,2 \pi] $$ oecurs when $$ x $$ is equal to $$ \begin{array}{llll}	ext { A. }-3 & 	ext { B. } 0 & 	ext { C. } \frac{\pi}{2} & 	ext { D, } \%\end{array} $$

UpStudy AI · Accepted Answer

To determine when the function $$ f(x) = -3 \cos x + 3 $$ attains its maximum value on the closed interval $$ [0, 2\pi] $$, let's analyze the function step by step.

### Step 1: Understand the Function
The function is given by:
$$ f(x) = -3 \cos x + 3 $$

### Step 2: Analyze the Cosine Component
The cosine function, $$ \cos x $$, oscillates between -1 and 1:
$$ -1 \leq \cos x \leq 1 $$

### Step 3: Determine the Range of $$ f(x) $$
Multiply the cosine function by -3:
$$ -3 \times \cos x $$
This inverts the cosine wave and scales it by a factor of 3:
$$ -3 \times 1 = -3 \quad \text{and} \quad -3 \times (-1) = 3 $$

Now, add 3 to shift the entire function upwards:
$$ f(x) = -3 \cos x + 3 $$
The range becomes:
$$ 0 \leq f(x) \leq 6 $$

### Step 4: Find the Maximum Value
The maximum value of $$ f(x) $$ is 6. This occurs when:
$$ -3 \cos x + 3 = 6 $$
$$ -3 \cos x = 3 $$
$$ \cos x = -1 $$

### Step 5: Determine $$ x $$ When $$ \cos x = -1 $$
The cosine function equals -1 at:
$$ x = \pi $$

### Conclusion
The function $$ f(x) $$ attains its maximum value of 6 at $$ x = \pi $$.

**Answer:**  
**Option D: $$ \pi $$**
The maximum value of $$ f(x) = -3 \cos x + 3 $$ on $$ [0, 2\pi] $$ occurs at $$ x = \pi $$.

Let
The maximum value attained by on the closed internal oecurs when is equal to

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