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What is the slope of the tangent line to the curve y = x^2 + 2x at x = 1?
What is the slope of the tangent line to the curve y = x^2 + 2x at x = 1?
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What is the slope of the tangent line to the curve y = x^2 + 2x at x = 1?
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The derivative y' = 2x + 2. At x = 1, y' = 2(1) + 2 = 4.
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 + 2x at x = 1?
Solution:
The derivative y' = 2x + 2. At x = 1, y' = 2(1) + 2 = 4.
Steps: 6
Show Steps
Step 1: Identify the function given in the question, which is y = x^2 + 2x.
Step 2: Find the derivative of the function. The derivative tells us the slope of the tangent line. For y = x^2 + 2x, the derivative is y' = 2x + 2.
Step 3: Substitute the value of x into the derivative to find the slope at that point. We need to find the slope at x = 1.
Step 4: Calculate y' at x = 1. Substitute 1 into the derivative: y' = 2(1) + 2.
Step 5: Simplify the expression: y' = 2 + 2 = 4.
Step 6: Conclude that the slope of the tangent line to the curve at x = 1 is 4.
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