Find all critical points of the function g(x) = 2x^3 - 9x^2 + 12x + 1.
Answer and explanation
Correct answer: D. x = 1 and x = 2
- Step 1: Take derivative: g'(x) = 6x^2 - 18x + 12. Step 2. Set g'(x) = 0: 6(x^2 - 3x + 2) = 0. Step 3. Factor: 6(x - 1)(x - 2) = 0 => x = 1 and x = 2. Answer: x = 1 and x = 2. Why not the others: -1 and -2 invert signs; 1 and 3 factor x^2 - 4x + 3.
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