A function satisfies f'(x) = 6x^2 - 4x and f(1) = 5. What is f(2)?

Answer and explanation

Correct answer: C. 13

  1. Step 1: f(x) = 2x^3 - 2x^2 + C. Step 2. f(1) = 2 - 2 + C = 5, so C = 5. Step 3. f(2) = 16 - 8 + 5 = 13. Answer: 13. Why not the others: 16: That is f'(2), the derivative, not f(2). 5: That is f(1). 8: That leaves out the constant of integration, C = 5.

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