Question: The slope of the tangent to the curve y = x^3 - 3x at x = 1 is:
Options:
0
1
2
3
Correct Answer: 1
Solution:
The derivative f\'(x) = 3x^2 - 3. At x = 1, f\'(1) = 3(1)^2 - 3 = 0, so the slope is 0.
The slope of the tangent to the curve y = x^3 - 3x at x = 1 is:
Practice Questions
Q1
The slope of the tangent to the curve y = x^3 - 3x at x = 1 is:
0
1
2
3
Questions & Step-by-Step Solutions
The slope of the tangent to the curve y = x^3 - 3x at x = 1 is:
Step 1: Identify the function given in the question, which is y = x^3 - 3x.
Step 2: Find the derivative of the function. The derivative tells us the slope of the tangent line. The derivative of y = x^3 - 3x is f'(x) = 3x^2 - 3.
Step 3: Substitute x = 1 into the derivative to find the slope at that point. Calculate f'(1) = 3(1)^2 - 3.
