Determine the critical points of the function f(x) = 2x^3 - 3x^2 - 12x + 5.
Answer and explanation
Correct answer: D. x = -1 and x = 2
- Step 1: Set the first derivative f'(x) = 6x^2 - 6x - 12 equal to zero.
- Step 2: Factor: 6(x^2 - x - 2) = 6(x - 2)(x + 1) = 0, giving roots x = 2 and x = -1.
Answer
x = -1 and x = 2.
Why not the others: 'x = 1 and x = -2' inverts the algebraic signs of the roots; 'x = 0 and x = 2' confuses y-intercept with stationary points; 'x = -1 and x = -2' has the wrong sign on the positive root.
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