If f'(x) = x^3 - 3x, what is f'(2)?

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Study for the AP Calculus BC Test. Discover flashcards and multiple choice questions with hints and explanations to prepare effectively. Ace your exam!

Multiple Choice

If f'(x) = x^3 - 3x, what is f'(2)?

Explanation:
Evaluating a derivative at a specific input is just substitution. Since f'(x) = x^3 - 3x, plug in x = 2: f'(2) = 2^3 - 3·2 = 8 - 6 = 2. This gives the slope of the original function at x = 2, i.e., the instantaneous rate of change there. The value is 2.

Evaluating a derivative at a specific input is just substitution. Since f'(x) = x^3 - 3x, plug in x = 2: f'(2) = 2^3 - 3·2 = 8 - 6 = 2. This gives the slope of the original function at x = 2, i.e., the instantaneous rate of change there. The value is 2.

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