What is the derivative of f(x) = 2x^3 - 9x^2 + 12x? (2021)

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Question: What is the derivative of f(x) = 2x^3 - 9x^2 + 12x? (2021)

Options:

Correct Answer: 6x^2 - 18x + 12

Exam Year: 2021

Solution:

f\'(x) = 6x^2 - 18x + 12.

What is the derivative of f(x) = 2x^3 - 9x^2 + 12x? (2021)

What is the derivative of f(x) = 2x^3 - 9x^2 + 12x? (2021)

Step 1: Identify the function f(x) = 2x^3 - 9x^2 + 12x.
Step 2: Use the power rule for derivatives, which states that if f(x) = ax^n, then f'(x) = n * ax^(n-1).
Step 3: Apply the power rule to each term in the function.
Step 4: For the first term 2x^3, the derivative is 3 * 2x^(3-1) = 6x^2.
Step 5: For the second term -9x^2, the derivative is 2 * -9x^(2-1) = -18x.
Step 6: For the third term 12x, the derivative is 1 * 12x^(1-1) = 12.
Step 7: Combine all the derivatives from each term: f'(x) = 6x^2 - 18x + 12.

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