What is the slope of the tangent line to the curve y = x^3 at x = 1? (2019)

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Question: What is the slope of the tangent line to the curve y = x^3 at x = 1? (2019)

Options:

Correct Answer: 3

Exam Year: 2019

Solution:

The derivative y\' = 3x^2. At x = 1, y\' = 3(1^2) = 3.

What is the slope of the tangent line to the curve y = x^3 at x = 1? (2019)

What is the slope of the tangent line to the curve y = x^3 at x = 1? (2019)

Step 1: Identify the function we are working with, which is y = x^3.
Step 2: Find the derivative of the function. The derivative tells us the slope of the tangent line. For y = x^3, the derivative is y' = 3x^2.
Step 3: Substitute the value of x into the derivative to find the slope at that point. We need to find the slope at x = 1.
Step 4: Calculate the derivative at x = 1. Substitute 1 into the derivative: y' = 3(1^2).
Step 5: Simplify the calculation: 1^2 = 1, so y' = 3(1) = 3.
Step 6: Conclude that the slope of the tangent line to the curve y = x^3 at x = 1 is 3.

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