What is the slope of the tangent line to the curve y = x^2 + 2x at x = 1?

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Question: What is the slope of the tangent line to the curve y = x^2 + 2x at x = 1?

Options:

Correct Answer: 3

Solution:

The derivative y\' = 2x + 2. At x = 1, y\' = 2(1) + 2 = 4.

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?

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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