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JEE Mains · Maths · STD 12 - 6. Application of derivatives
The function/ defined by \(f(x)\, = x^3 - 3x^2 + 5x + 7\), is
- A increasing in \(R\).
- B decreasing in \(R\)
- C decreasing in \(\left( {0,\infty } \right)\) and increasing in \(\left( { - \infty ,0} \right)\)
- D increasing in \(\left( {0,\infty } \right)\) and decreasing in \(\left( { - \infty ,0} \right)\)
Answer & Solution
Correct Answer
(A) increasing in \(R\).
Step-by-step Solution
Detailed explanation
\(f(x)=x^{3}-3 x^{2}+5 x+7\) For increasing \(f^{\prime}(x)=3 x^{2}-6 x+5>0\) For decreasing \(f^{\prime}(x)=3 x^{2}-6 x+5<0\) \(x \in R\)
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