KVPY SX SB Exam 2016 Question Paper

Question : 82 of 120

Marks: +1, -0

The range of the polynomial

p(x) = 4x^3- 3x

as x varies over the interval

(-1/2,1/2)

Solution:

P'(x) = 12x^2 - 3 = 3 (4x^2 - 1)

(-1/2,1/2)

P'(x) < 0
⇒ P(x) is decreasing
⇒ Range ∈ (P(–1), P(1))
Range ∈ (–1, 1)

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