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

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Question: What is the slope of the tangent line to the curve y = x^2 at the point (1,1)? (2023)

Options:

Correct Answer: 2

Exam Year: 2023

Solution:

The derivative y\' = 2x; At x = 1, slope = 2(1) = 2.

What is the slope of the tangent line to the curve y = x^2 at the point (1,1)? (2023)

What is the slope of the tangent line to the curve y = x^2 at the point (1,1)? (2023)

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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