MCQ
Function $f(x) = x^3 - 27x + 5$ is monotonically increasing when:
- A$\text{x}<-3$
- B$|\text{x}|>3$
- C$\text{x}\leq-3$
- ✓$|\text{x}|\geq3$
✓
Answer
Correct option: D.
$|\text{x}|\geq3$
$f(x) = 3x^2 - 27x$
$\Rightarrow f'(x) = x^3 - 27x + 5$
$\Rightarrow f'(x) = 3(x^2 - 9)$
Function is increasing,
$3\big(\text{x}^2-9\big)\geq0$
$\Rightarrow\text{x}^2\geq9$
$\Rightarrow|\text{x}|\geq3$
$\Rightarrow f'(x) = x^3 - 27x + 5$
$\Rightarrow f'(x) = 3(x^2 - 9)$
Function is increasing,
$3\big(\text{x}^2-9\big)\geq0$
$\Rightarrow\text{x}^2\geq9$
$\Rightarrow|\text{x}|\geq3$
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