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

₹0.0

Question: What is the slope of the tangent line to the curve y = x^2 + 2x at the point (1, 3)?

Options:

Correct Answer: 2

Solution:

The derivative y\' = 2x + 2. At x = 1, y\' = 2(1) + 2 = 4, which is the slope of the tangent line.

What is the slope of the tangent line to the curve y = x^2 + 2x at the point (1, 3)?

What is the slope of the tangent line to the curve y = x^2 + 2x at the point (1, 3)?

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: Determine the x-coordinate of the point where we want to find the slope. In this case, the point is (1, 3), 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: Simplify the calculation: 2(1) + 2 = 2 + 2 = 4.
Step 6: Conclude that the slope of the tangent line to the curve at the point (1, 3) is 4.

No concepts available.