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What is the slope of the tangent line to the curve y = x^2 at the point (3, 9)?

Practice Questions

Q1
What is the slope of the tangent line to the curve y = x^2 at the point (3, 9)? (2020)
  1. 3
  2. 6
  3. 9
  4. 12

Questions & Step-by-Step Solutions

What is the slope of the tangent line to the curve y = x^2 at the point (3, 9)? (2020)
  • Step 1: Identify the function given, 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 (3, 9), so x = 3.
  • Step 4: Substitute x = 3 into the derivative to find the slope at that point. Calculate y' = 2(3).
  • Step 5: Perform the multiplication: 2(3) = 6.
  • Step 6: Conclude that the slope of the tangent line to the curve at the point (3, 9) is 6.
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