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2025 PEA Q16

f(x)=4x3−6x2−72xf(x) = 4x^3 - 6x^2 - 72x. Where is ff increasing / decreasing?

Reveal answer and solution

Answer

D

Solution

  1. 1
    f′(x)=12x2−12x−72=12(x2−x−6)=12(x−3)(x+2). f'(x) = 12 x^2 - 12 x - 72 = 12(x^2 - x - 6) = 12(x-3)(x+2).
  2. 2

    Sign of f′f': positive for x<−2x<-2, negative for −2<x<3-2<x<3, positive for x>3x>3.

Answer structure / marking notes

Factor the derivative completely to read off the sign chart.

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2025/ISI_MSQE_PEA_2025_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.