JEE Mains · Maths · STD 12 - 6. Application of derivatives
The function, \(f(x)=(3 x-7) x^{2 / 3}, x \in R,\) is increasing for all \(x\) lying in
- A \((-\infty, 0) \cup\left(\frac{3}{7}, \infty\right)\)
- B \((-\infty, 0) \cup\left(\frac{14}{15}, \infty\right)\)
- C \(\left(-\infty, \frac{14}{15}\right)\)
- D \(\left(-\infty,-\frac{14}{15}\right) \cup(0, \infty)\)
Answer & Solution
Correct Answer
(B) \((-\infty, 0) \cup\left(\frac{14}{15}, \infty\right)\)
Step-by-step Solution
Detailed explanation
\(f(x)=(3 x-7) x^{2 / 3}\) \(\Rightarrow \quad f(x)=3 x^{5 / 3}-7 x^{2 / 3}\) \(\Rightarrow \quad f^{\prime}(x)=5 x^{2 / 3}-\frac{14}{3 x^{1 / 3}}\) \(=\frac{15 x-14}{3 x^{1 / 3}}>0\)…
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