COMEDK · Maths · 27. Application of Derivatives
The function \(f(x)=5+36 x+3 x^{2}-2 x^{3}\) is increasing in the interval
- A \((-2,3)\)
- B \((2,3)\)
- C \([2,3)\)
- D \((2,3]\)
Answer & Solution
Correct Answer
(A) \((-2,3)\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=5+36 x+3 x^{2}-2 x^{3}\) \(\Rightarrow f^{\prime}(x)=36+6 x-6 x^{2}\) \(=-6\left(x^{2}-x-6\right)\) \(=-6\left(x^{2}-3 x+2 x-6\right)\) \(=-6(x-3)(x+2)\) For increasing function, \(f^{\prime}(x)>0\) \(\Rightarrow \quad(x-3)(x+2) -2\) \(\Rightarrow \quad-2 < x < 3\)…
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