Question:
The interval in which the function \(2x^3+15\) increases less rapidly than the function \(9x^2-12x\), is
The interval in which the function \(2x^3+15\) increases less rapidly than the function \(9x^2-12x\), is
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Compare derivatives to compare growth rates.
Updated On: Mar 24, 2026
- \((-\infty,1)\)
- \((1,2)\)
- \((2,\infty)\)
- None of these
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The Correct Option is A
Solution and Explanation
Step 1: Compare derivatives:
\[ (2x^3+15)' = 6x^2,\quad (9x^2-12x)' = 18x-12 \]
Step 2:
\[ 6x^2 < 18x-12 \Rightarrow x < 1 \]
\[ (2x^3+15)' = 6x^2,\quad (9x^2-12x)' = 18x-12 \]
Step 2:
\[ 6x^2 < 18x-12 \Rightarrow x < 1 \]
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