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If f(x) = e^x - x^2, find the x-coordinate of the local maximum.
If f(x) = e^x - x^2, find the x-coordinate of the local maximum.
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If f(x) = e^x - x^2, find the x-coordinate of the local maximum.
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Find f'(x) = e^x - 2x. Setting f'(x) = 0 gives a local maximum at x = 1.
Questions & Step-by-step Solutions
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Q: If f(x) = e^x - x^2, find the x-coordinate of the local maximum.
Solution:
Find f'(x) = e^x - 2x. Setting f'(x) = 0 gives a local maximum at x = 1.
Steps: 6
Show Steps
Step 1: Start with the function f(x) = e^x - x^2.
Step 2: Find the derivative of the function, which is f'(x) = e^x - 2x.
Step 3: Set the derivative equal to zero to find critical points: e^x - 2x = 0.
Step 4: Solve the equation e^x = 2x. This may require numerical methods or graphing.
Step 5: Check the critical points to determine if they are local maxima or minima.
Step 6: After checking, you find that x = 1 is a local maximum.
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