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What is the slope of the tangent line to the curve y = x^2 at the point (2, 4)?

Practice Questions

Q1
What is the slope of the tangent line to the curve y = x^2 at the point (2, 4)?
  1. 2
  2. 4
  3. 3
  4. 1

Questions & Step-by-Step Solutions

What is the slope of the tangent line to the curve y = x^2 at the point (2, 4)?
  • Step 1: Identify the function given in the question, which is y = x^2.
  • Step 2: Find the derivative of the function. The derivative of y = x^2 is y' = 2x.
  • Step 3: Determine the x-coordinate of the point where we want to find the slope. The point given is (2, 4), so x = 2.
  • Step 4: Substitute x = 2 into the derivative to find the slope at that point. Calculate y'(2) = 2(2).
  • Step 5: Perform the multiplication: 2(2) = 4. This means the slope of the tangent line at the point (2, 4) is 4.
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