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Determine the point where the function f(x) = 4x - x^2 has a maximum. (2022)
Determine the point where the function f(x) = 4x - x^2 has a maximum. (2022)
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Q1
Determine the point where the function f(x) = 4x - x^2 has a maximum. (2022)
(0, 0)
(2, 4)
(1, 3)
(3, 3)
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The maximum occurs at x = 2, found by setting f'(x) = 4 - 2x = 0. f(2) = 4(2) - (2^2) = 4.
Questions & Step-by-step Solutions
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Q: Determine the point where the function f(x) = 4x - x^2 has a maximum. (2022)
Solution:
The maximum occurs at x = 2, found by setting f'(x) = 4 - 2x = 0. f(2) = 4(2) - (2^2) = 4.
Steps: 7
Show Steps
Step 1: Write down the function f(x) = 4x - x^2.
Step 2: Find the derivative of the function, which is f'(x) = 4 - 2x.
Step 3: Set the derivative equal to zero to find critical points: 4 - 2x = 0.
Step 4: Solve for x: 2x = 4, so x = 2.
Step 5: To find the maximum value, substitute x = 2 back into the original function: f(2) = 4(2) - (2^2).
Step 6: Calculate f(2): f(2) = 8 - 4 = 4.
Step 7: The maximum point of the function is at (2, 4).
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