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Function signs

CMAT 2019 · Quantitative Techniques & Data Interpretation · Medium · Functions

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If f(x)=x3−4x+pf(x) = x^3 - 4x + p and f(0)f(0) and f(1)f(1) are of opposite signs, which one of the following is necessarily true?

  1. A.

    −1<p<2-1 < p < 2

  2. B.

    0<p<30 < p < 3

  3. C.

    −2<p<1-2 < p < 1

  4. D.

    −3<p<0-3 < p < 0

Answer

B

Explanation

f(0)=pf(0) = p f(1)=1−4+p=p−3f(1) = 1 - 4 + p = p - 3 Since f(0)f(0) and f(1)f(1) have opposite signs, f(0)⋅f(1)<0f(0) \cdot f(1) < 0. p(p−3)<0  ⟹  0<p<3p(p - 3) < 0 \implies 0 < p < 3

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