AP EAMCET · Maths · Application of Derivatives
The interval in which the function \(f(x)=\frac{\log (7+x)}{\log (3+x)}(x>0)\) decreases is
- A \(\left(0, \frac{7}{3}\right)\)
- B \(\left(0, \frac{3}{7}\right)\)
- C \((0,1)\)
- D \((0, \infty)\)
Answer & Solution
Correct Answer
(D) \((0, \infty)\)
Step-by-step Solution
Detailed explanation
If the given function \(f(x)=\frac{\log (7+x)}{\log (3+x)}, x > 0\) is decreasing function then \(f^{\prime}(x) 0\). \(\Rightarrow \quad x \in(0, \infty)\) Hence, option (d) is correct.
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