What is the derivative of f(x) = x^3 - 4x + 7? (2021)

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Question: What is the derivative of f(x) = x^3 - 4x + 7? (2021)

Options:

Correct Answer: 3x^2 - 4

Exam Year: 2021

Solution:

Using the power rule, f\'(x) = 3x^2 - 4.

What is the derivative of f(x) = x^3 - 4x + 7? (2021)

What is the derivative of f(x) = x^3 - 4x + 7? (2021)

Step 1: Identify the function f(x) = x^3 - 4x + 7.
Step 2: Recognize that we need to find the derivative, which tells us the rate of change of the function.
Step 3: Use the power rule for derivatives, which states that if f(x) = x^n, then f'(x) = n*x^(n-1).
Step 4: Apply the power rule to each term in the function: For x^3, the derivative is 3*x^(3-1) = 3x^2.
Step 5: For the term -4x, the derivative is -4 (since the derivative of x is 1).
Step 6: The constant term 7 has a derivative of 0 (since constants do not change).
Step 7: Combine the derivatives from Steps 4, 5, and 6: f'(x) = 3x^2 - 4 + 0.
Step 8: Simplify the expression to get the final result: f'(x) = 3x^2 - 4.

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