AP EAMCET · Maths · Application of Derivatives
If \(f(x)=\sqrt{x}\) and \(g(x)=\frac{1}{\sqrt{x}}\) for \(x \in[3,12]\), then the value of \(c \in(3,12)\) for which \(\frac{f^{\prime}(c)}{g^{\prime}(c)}=\frac{f(12)-f(3)}{g(12)-g(3)}\) holds, is
- A 7.5
- B 4.8
- C 6
- D 9
Answer & Solution
Correct Answer
(C) 6
Step-by-step Solution
Detailed explanation
Given, \(f(x)=x^{1 / 2}\) \[ \begin{array}{cc} f^{\prime}(x)=\frac{1}{2} x^{-\frac{1}{2}} & \\ f^{\prime}(c)=\frac{1}{2} c^{-\frac{1}{2}}, & g(x)=x^{-\frac{1}{2}} \\ g^{\prime}(x)=\frac{-1}{2} x^{-\frac{3}{2}} & g^{\prime}(c)=-\frac{1}{2} c^{-\frac{3}{2}} \end{array} \] Now,…
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