Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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![### Finding the Critical Number of a Function
Determine the critical number of the given function:
\[ f(x) = (6x - 3)e^{5x} \]
### Task
The function \( f(x) = (6x - 3)e^{5x} \) has one critical number. Find it.
### Solution
To find the critical number, solve for \( x \) where \( f'(x) = 0 \):
\[ x = \text{[Input box for answer]} \]
### Instructions
1. Differentiate the function \( f(x) \) to find \( f'(x) \).
2. Set the derivative equal to zero and solve for \( x \).
3. Verify the solution to ensure it is a critical number.
### Interactive Element
Enter the value of \( x \) where \( f'(x) = 0 \):
\[ x = \text{[Input box for answer]} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f65933a-ca3b-4974-83ff-08bb4a6985ce%2F920a0685-3592-43ab-8866-711d95e9ee94%2Fzo83mtx_processed.png&w=3840&q=75)
Transcribed Image Text:### Finding the Critical Number of a Function
Determine the critical number of the given function:
\[ f(x) = (6x - 3)e^{5x} \]
### Task
The function \( f(x) = (6x - 3)e^{5x} \) has one critical number. Find it.
### Solution
To find the critical number, solve for \( x \) where \( f'(x) = 0 \):
\[ x = \text{[Input box for answer]} \]
### Instructions
1. Differentiate the function \( f(x) \) to find \( f'(x) \).
2. Set the derivative equal to zero and solve for \( x \).
3. Verify the solution to ensure it is a critical number.
### Interactive Element
Enter the value of \( x \) where \( f'(x) = 0 \):
\[ x = \text{[Input box for answer]} \]
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