My Learning Cart
?
Categories
Account

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

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

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

Options:

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

Correct Answer: 3

Solution: 

Calculating the derivative f\'(x) = 2x + 2, we find f\'(1) = 4.

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

Practice Questions

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

Questions & Step-by-Step Solutions

If f(x) = x^2 + 2x + 1, what is f'(1)?
  • Step 1: Identify the function f(x) = x^2 + 2x + 1.
  • Step 2: Find the derivative of the function f(x). The derivative f'(x) tells us the rate of change of f(x).
  • Step 3: Use the power rule to differentiate each term: The derivative of x^2 is 2x, the derivative of 2x is 2, and the derivative of 1 is 0.
  • Step 4: Combine the derivatives to get f'(x) = 2x + 2.
  • Step 5: Now, we need to find f'(1). Substitute x = 1 into the derivative: f'(1) = 2(1) + 2.
  • Step 6: Calculate f'(1): 2(1) + 2 = 2 + 2 = 4.
  • Derivative Calculation – The question tests the ability to find the derivative of a polynomial function and evaluate it at a specific point.
  • Function Evaluation – It assesses the understanding of substituting a value into a derived function.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks