What is the derivative of f(x) = 7x^2 + 2x - 5? (2023)

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Question: What is the derivative of f(x) = 7x^2 + 2x - 5? (2023)

Options:

Correct Answer: 14x + 2

Exam Year: 2023

Solution:

Using the power rule, f\'(x) = 14x + 2.

What is the derivative of f(x) = 7x^2 + 2x - 5? (2023)

What is the derivative of f(x) = 7x^2 + 2x - 5? (2023)

Step 1: Identify the function f(x) = 7x^2 + 2x - 5.
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) = ax^n, then f'(x) = n * ax^(n-1).
Step 4: Apply the power rule to the first term 7x^2: The derivative is 2 * 7 * x^(2-1) = 14x.
Step 5: Apply the power rule to the second term 2x: The derivative is 1 * 2 * x^(1-1) = 2.
Step 6: The third term -5 is a constant, and the derivative of a constant is 0.
Step 7: Combine the derivatives from Steps 4, 5, and 6: f'(x) = 14x + 2 + 0.
Step 8: Simplify the expression: f'(x) = 14x + 2.

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