CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
For the function f(x) = 2x^3 - 9x^2 + 12x + 5, which statement about its stationary points is correct?
The function has a maximum at x = 1 and a minimum at x = 2. The first derivative factorises as 6(x-1)(x-2), and the second derivative 12x - 18 is negative at x = 1 and positive at x = 2.
- AMaximum at x = 1 and minimum at x = 2Correct
- BMinimum at x = 1 and maximum at x = 2
- CMaximum at both x = 1 and x = 2
- DMinimum at both x = 1 and x = 2
Explanation
f'(x) = 6x^2 - 18x + 12 = 6(x-1)(x-2), so stationary points are x = 1 and 2. f''(x) = 12x - 18: at x = 1 it is -6 (maximum); at x = 2 it is 6 (minimum). The reversed option comes from swapping the sign test.
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