MHT CET · Maths · Application of Derivatives
The function \(f(x)=2 x^3-9 x^2+12 x+29\) is monotonically increasing in the interval
- A \((-\infty, 1) \cup(2, \infty)\)
- B \((-\infty, \infty)\)
- C \((2, \infty)\)
- D \((-\infty, 1)\)
Answer & Solution
Correct Answer
(A) \((-\infty, 1) \cup(2, \infty)\)
Step-by-step Solution
Detailed explanation
\(f(x)=2 x^3-9 x^2+12 x+29\)
\(\Rightarrow f^{\prime}(x)=6 x^2-18 x+12=6(x-1)(x-2)\) sign scheme
\(\Rightarrow f(x)\) is increasing in the interval
\(x \varepsilon(\infty-, 1) \cup(2, \infty)\)
\(\Rightarrow f^{\prime}(x)=6 x^2-18 x+12=6(x-1)(x-2)\) sign scheme
\(\Rightarrow f(x)\) is increasing in the interval
\(x \varepsilon(\infty-, 1) \cup(2, \infty)\)
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