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

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

Options:

  1. 8
  2. 10
  3. 13
  4. 15

Correct Answer: 10

Solution: 

f\'(x) = 10x + 3; f\'(1) = 10*1 + 3 = 13.

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

Practice Questions

Q1
If f(x) = 5x^2 + 3x, what is f'(1)?
  1. 8
  2. 10
  3. 13
  4. 15

Questions & Step-by-Step Solutions

If f(x) = 5x^2 + 3x, what is f'(1)?
  • Step 1: Identify the function f(x) = 5x^2 + 3x.
  • Step 2: Find the derivative of the function, which is f'(x).
  • Step 3: Use the power rule to differentiate: The derivative of 5x^2 is 10x, and the derivative of 3x is 3.
  • Step 4: Combine the derivatives to get f'(x) = 10x + 3.
  • Step 5: Now, substitute x = 1 into the derivative: f'(1) = 10*1 + 3.
  • Step 6: Calculate the result: 10*1 = 10, then add 3 to get 13.
  • Differentiation – The process of finding the derivative of a function.
  • Evaluation of Derivatives – Substituting a specific value into the derivative to find the slope at that point.
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