The slope of the tangent line to the curve y = x^2 at the point (2, 4) is: (2022

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Question: The slope of the tangent line to the curve y = x^2 at the point (2, 4) is: (2022)

Options:

Correct Answer: 2

Exam Year: 2022

Solution:

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

The slope of the tangent line to the curve y = x^2 at the point (2, 4) is: (2022)

The slope of the tangent line to the curve y = x^2 at the point (2, 4) is: (2022)

Step 1: Identify the function given in the question, which is y = x^2.
Step 2: Understand that the slope of the tangent line at a point on the curve is found using the derivative of the function.
Step 3: Calculate the derivative of y = x^2. The derivative is y' = 2x.
Step 4: Find the x-coordinate of the point where we want to find the slope, which is x = 2.
Step 5: Substitute x = 2 into the derivative y' = 2x to find the slope at that point.
Step 6: Calculate y' = 2(2) = 4.
Step 7: Conclude that the slope of the tangent line to the curve y = x^2 at the point (2, 4) is 4.

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