Question:
The function \( f(x) = 2x^3 - 3x^2 - 36x + 28 \) is increasing in
The function \( f(x) = 2x^3 - 3x^2 - 36x + 28 \) is increasing in
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Factor derivative completely, then use sign chart.
Updated On: Apr 21, 2026
- \( (-\infty,-1] \cup [3,\infty) \)
- \( (-\infty,-2] \cup [3,\infty) \)
- \( (-\infty,-2] \cup [5,\infty) \)
- \( (-\infty,-5] \cup [3,\infty) \)
- \( (-\infty,-2] \cup [8,\infty) \)
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The Correct Option is B
Solution and Explanation
Concept:
Increasing where \( f'(x)>0 \).
Step 1: Differentiate.
\[ f'(x) = 6x^2 - 6x - 36 \] \[ = 6(x^2 - x - 6) = 6(x-3)(x+2) \]
Step 2: Sign analysis.
\[ f'(x)>0 \Rightarrow x3 \]
Step 1: Differentiate.
\[ f'(x) = 6x^2 - 6x - 36 \] \[ = 6(x^2 - x - 6) = 6(x-3)(x+2) \]
Step 2: Sign analysis.
\[ f'(x)>0 \Rightarrow x3 \]
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