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For the function f(x) = x^2 + 2x, find the local maximum. (2022)

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Question: For the function f(x) = x^2 + 2x, find the local maximum. (2022)

Options:

  1. -1
  2. 0
  3. 1
  4. 2

Correct Answer: -1

Solution: 

f\'(x) = 2x + 2. Setting f\'(x) = 0 gives x = -1. f(-1) = 1.

For the function f(x) = x^2 + 2x, find the local maximum. (2022)

Practice Questions

Q1
For the function f(x) = x^2 + 2x, find the local maximum. (2022)
  1. -1
  2. 0
  3. 1
  4. 2

Questions & Step-by-Step Solutions

For the function f(x) = x^2 + 2x, find the local maximum. (2022)
  • 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.
  • Finding Local Extrema – The process of determining local maximum and minimum values of a function using its derivative.
  • Critical Points – Points where the derivative is zero or undefined, which are candidates for local extrema.
  • Second Derivative Test – A method to determine the nature of critical points by evaluating the second derivative.
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