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Find the slope of the tangent line to f(x) = x^2 + 2x at x = 1. (2022)

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Question: Find the slope of the tangent line to f(x) = x^2 + 2x at x = 1. (2022)

Options:

  1. 2
  2. 3
  3. 4
  4. 5

Correct Answer: 2

Exam Year: 2022

Solution: 

f\'(x) = 2x + 2. At x = 1, f\'(1) = 4.

Find the slope of the tangent line to f(x) = x^2 + 2x at x = 1. (2022)

Practice Questions

Q1
Find the slope of the tangent line to f(x) = x^2 + 2x at x = 1. (2022)
  1. 2
  2. 3
  3. 4
  4. 5

Questions & Step-by-Step Solutions

Find the slope of the tangent line to f(x) = x^2 + 2x at x = 1. (2022)
  • Step 1: Identify the function f(x) = x^2 + 2x.
  • Step 2: Find the derivative of the function, which gives the slope of the tangent line. The derivative f'(x) is calculated as follows: f'(x) = 2x + 2.
  • Step 3: Substitute x = 1 into the derivative to find the slope at that point. So, f'(1) = 2(1) + 2.
  • Step 4: Calculate f'(1). This gives f'(1) = 2 + 2 = 4.
  • Step 5: The slope of the tangent line to the function at x = 1 is 4.
  • Derivative – The slope of the tangent line to a function at a given point is found using the derivative of the function.
  • Evaluation of Derivative – Substituting the specific x-value into the derivative to find the slope at that point.
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