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For the function f(x) = x^2 + 2x, find the local maximum. (2022)
For the function f(x) = x^2 + 2x, find the local maximum. (2022)
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For the function f(x) = x^2 + 2x, find the local maximum. (2022)
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f'(x) = 2x + 2. Setting f'(x) = 0 gives x = -1. f(-1) = 1.
Questions & Step-by-step Solutions
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Q: For the function f(x) = x^2 + 2x, find the local maximum. (2022)
Solution:
f'(x) = 2x + 2. Setting f'(x) = 0 gives x = -1. f(-1) = 1.
Steps: 6
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Step 1: Write down the function f(x) = x^2 + 2x.
Step 2: Find the derivative of the function, which is f'(x) = 2x + 2.
Step 3: Set the derivative equal to zero to find critical points: 2x + 2 = 0.
Step 4: Solve for x: 2x = -2, so x = -1.
Step 5: To find the local maximum, evaluate the function at x = -1: f(-1) = (-1)^2 + 2(-1) = 1.
Step 6: The local maximum value of the function is 1 at x = -1.
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