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CGP EDU Academic Team
Published on: August 14, 2026
If M be the greatest value and m be the least value of
ƒ(x) = 2x 3 – 3x 2 – 12x + 1, for –1 ≤ x ≤ 3/2, then the ordered pair (M, m) is -
Text Solution
Verified by ExpertsThe correct answer is:
B
ƒ(x) = 2x 3 – 3x 2 – 12x + 1
ƒ ′ (x) = 6(x 2 – x – 2) = 0 for x = –1, x = 2
But x = 2 is outside the interval [–1, 3/2] :
for –1 < x < 3/2 ; ƒ ′ (x) < 0.
f(x) is decreasing.
M = ƒ(–1) = –2 – 3 + 12 + 1 = 8; m = f(3/2) = –17.
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