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CGP EDU Academic Team
Published on: August 12, 2026
The function f : [0, 3] → [1, 29], defined by f(x) = 2x 3 – 15x 2 + 36x + 1, is
Text Solution
Verified by ExpertsThe correct answer is:
B
F : [0, 3] → [1, 29]
f(x) = 2x 3 – 15x 2 + 36 x + 1
f ′ (x) = 6x 2 – 30 x + 36 = 6(x 2 – 5x + 6) = 6(x – 2) (x – 3)
in given domain function has local maxima, it is many-one
Now at x = 0 f(0) = 1
x = 2 f(b) = 16 – 60 + 72 + 1 = 29
x = 3 f(c) = 54 – 135 + 108 + 1 = 163 – 135 = 28
Has range = [1, 29]
Hence given function is onto
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