GATE CSE 2023 Q28: Local extrema of f(x) = x³ + 15x² − 33x − 36

Let

$f(x) = x^3 + 15x^2 - 33x - 36$

be a real-valued function.

Which of the following statements is/are TRUE?

Try it: multiple select: one or more correct options

Select all correct options. No negative marking, no partial marks.

Show answer and explanation

Answer: B, D (official GATE 2023 final answer key)

Concept used: Critical points from $f'(x) = 0$ , classified by the sign of $f''(x)$ .

First step: Solve $f'(x) = 3x^2 + 30x - 33 = 0$ , i.e. $(x + 11)(x - 1) = 0$ .

Full step-by-step solution

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Source: official GATE 2023 CS question paper and final answer key, organised by IIT Kanpur. Question paper · Answer key