What is the slope of the tangent to the curve y = x^2 + 2x at x = 1? (2023)
Practice Questions
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What is the slope of the tangent to the curve y = x^2 + 2x at x = 1? (2023)
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Questions & Step-by-Step Solutions
What is the slope of the tangent to the curve y = x^2 + 2x at x = 1? (2023)
Step 1: Identify the function given in the question, which is y = x^2 + 2x.
Step 2: Recognize that we need to find the slope of the tangent line at a specific point, which is at x = 1.
Step 3: To find the slope of the tangent, we need to calculate the derivative of the function. The derivative tells us the slope at any point on the curve.
Step 4: Differentiate the function y = x^2 + 2x. The derivative f'(x) is found using the power rule: f'(x) = 2x + 2.
Step 5: Now, we need to find the slope at x = 1. Substitute x = 1 into the derivative: f'(1) = 2(1) + 2.
Step 6: Calculate the result: f'(1) = 2 + 2 = 4.
Step 7: The slope of the tangent to the curve at x = 1 is 4.
