What is the slope of the tangent line to the curve y = x^2 at the point (3, 9)?

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Question: What is the slope of the tangent line to the curve y = x^2 at the point (3, 9)? (2020)

Options:

Correct Answer: 6

Exam Year: 2020

Solution:

The derivative y\' = 2x. At x = 3, y\' = 2(3) = 6.

What is the slope of the tangent line to the curve y = x^2 at the point (3, 9)? (2020)

What is the slope of the tangent line to the curve y = x^2 at the point (3, 9)? (2020)

Step 1: Identify the function given, 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 (3, 9), so x = 3.
Step 4: Substitute x = 3 into the derivative to find the slope at that point. Calculate y' = 2(3).
Step 5: Perform the multiplication: 2(3) = 6.
Step 6: Conclude that the slope of the tangent line to the curve at the point (3, 9) is 6.

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