What is the slope of the tangent line to the curve y = x^2 at the point (2, 4)?

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Question: What is the slope of the tangent line to the curve y = x^2 at the point (2, 4)?

Options:

Correct Answer: 2

Solution:

The derivative y\' = 2x. At x = 2, the slope is y\'(2) = 2(2) = 4.

What is the slope of the tangent line to the curve y = x^2 at the point (2, 4)?

What is the slope of the tangent line to the curve y = x^2 at the point (2, 4)?

Step 1: Identify the function given in the question, which is y = x^2.
Step 2: Find the derivative of the function. The derivative of y = x^2 is y' = 2x.
Step 3: Determine the x-coordinate of the point where we want to find the slope. The point given is (2, 4), so x = 2.
Step 4: Substitute x = 2 into the derivative to find the slope at that point. Calculate y'(2) = 2(2).
Step 5: Perform the multiplication: 2(2) = 4. This means the slope of the tangent line at the point (2, 4) is 4.

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