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If f(x) = 5x^2 + 3x - 1, what is f'(2)? (2020)

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Question: If f(x) = 5x^2 + 3x - 1, what is f\'(2)? (2020)

Options:

  1. 27
  2. 23
  3. 22
  4. 20

Correct Answer: 27

Exam Year: 2020

Solution: 

First, find f\'(x) = 10x + 3. Then, f\'(2) = 10(2) + 3 = 20 + 3 = 23.

If f(x) = 5x^2 + 3x - 1, what is f'(2)? (2020)

Practice Questions

Q1
If f(x) = 5x^2 + 3x - 1, what is f'(2)? (2020)
  1. 27
  2. 23
  3. 22
  4. 20

Questions & Step-by-Step Solutions

If f(x) = 5x^2 + 3x - 1, what is f'(2)? (2020)
  • Step 1: Identify the function f(x) = 5x^2 + 3x - 1.
  • Step 2: Find the derivative of the function, f'(x). The derivative of 5x^2 is 10x, and the derivative of 3x is 3. The derivative of -1 is 0.
  • Step 3: Combine the derivatives to get f'(x) = 10x + 3.
  • Step 4: Substitute x = 2 into the derivative: f'(2) = 10(2) + 3.
  • Step 5: Calculate 10(2) which equals 20.
  • Step 6: Add 20 and 3 to get 23.
  • Differentiation – Understanding how to find the derivative of a polynomial function.
  • Function Evaluation – Evaluating the derivative at a specific point.
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