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Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x) = 2x³ − 9x² + 12x + 5 in the interval [0, 3]. Then M − m is equal to -
- 1
- 5
- 4
- 9
Correct answer: 9
Solution
f'(x) = 6(x-1)(x-2), critical points x=1,2. f(0)=5, f(1)=10, f(2)=9, f(3)=14. On [0,3], M = 14 and m = 5, so M - m = 9.
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