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What is the slope of the tangent line to the curve y = x^2 at the point (1,1)? (
What is the slope of the tangent line to the curve y = x^2 at the point (1,1)? (2023)
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What is the slope of the tangent line to the curve y = x^2 at the point (1,1)? (2023)
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The derivative y' = 2x; At x = 1, slope = 2(1) = 2.
Questions & Step-by-step Solutions
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Q
Q: What is the slope of the tangent line to the curve y = x^2 at the point (1,1)? (2023)
Solution:
The derivative y' = 2x; At x = 1, slope = 2(1) = 2.
Steps: 5
Show Steps
Step 1: Identify the function given, which is y = x^2.
Step 2: Find the derivative of the function. The derivative tells us the slope of the tangent line. For y = x^2, the derivative is y' = 2x.
Step 3: Determine the x-coordinate of the point where we want to find the slope. The point given is (1, 1), so x = 1.
Step 4: Substitute x = 1 into the derivative to find the slope at that point. Calculate y' = 2(1) = 2.
Step 5: Conclude that the slope of the tangent line to the curve y = x^2 at the point (1, 1) is 2.
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