JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(f: R \rightarrow R\) be defined as \(f(\mathrm{x})= -\frac{4}{3} x^{3}+2 x^{2}+3 x ,\quad x>0\) \(\quad\quad\quad\quad 3 x e^{x}, \quad\quad\quad\quad\quad\quad\mathrm{x} \leq 0\) Then \(\mathrm{f}\) is increasing function in the interval.
- A \(\left(-1, \frac{3}{2}\right)\)
- B \(\left(\frac{-1}{2}, 2\right)\)
- C \((0,2)\)
- D \((-3,-1)\)
Answer & Solution
Correct Answer
(A) \(\left(-1, \frac{3}{2}\right)\)
Step-by-step Solution
Detailed explanation
For \(x\,>\,0 f^{\prime}(x)=-4 x^{2}+4 x+3\) \(\mathrm{F}(\mathrm{x})\) is increasing in \(\left(-\frac{1}{2}, \frac{3}{2}\right)\) For \(x \leq 0 f^{\prime}(x)=3 e^{x}(1+x)\) \(\mathrm{F}^{\prime}(\mathrm{x})>0 \forall \mathrm{x} \in(-1,0)\) \(\Rightarrow f(x)\) is increasing…
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