What is the value of the derivative of f(x) = 3x^3 - 2x at x = 1?

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Question: What is the value of the derivative of f(x) = 3x^3 - 2x at x = 1?

Options:

Correct Answer: 7

Solution:

f\'(x) = 9x^2 - 2. At x = 1, f\'(1) = 9*1^2 - 2 = 7.

What is the value of the derivative of f(x) = 3x^3 - 2x at x = 1?

What is the value of the derivative of f(x) = 3x^3 - 2x at x = 1?

Step 1: Identify the function f(x) = 3x^3 - 2x.
Step 2: Find the derivative of the function f(x). The derivative is denoted as f'(x).
Step 3: Use the power rule to differentiate each term: The derivative of 3x^3 is 9x^2, and the derivative of -2x is -2.
Step 4: Combine the derivatives to get f'(x) = 9x^2 - 2.
Step 5: Substitute x = 1 into the derivative f'(x). So, calculate f'(1) = 9*1^2 - 2.
Step 6: Calculate 1^2, which is 1. Then multiply by 9 to get 9.
Step 7: Subtract 2 from 9 to get the final result: 9 - 2 = 7.

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