A) \[-1\]
B) \[1\]
C) \[0\]
D) \[a\]
Correct Answer: C
Solution :
Given,\[f(x)=\sqrt{ax}+\frac{{{a}^{2}}}{\sqrt{ax}}\], Then,\[f'(x)=\frac{\sqrt{a}}{2\sqrt{x}}+\frac{{{a}^{2}}}{\sqrt{a}}\left( -\frac{1}{2}{{x}^{-3/2}} \right)\] \[\Rightarrow \] \[f'(x)=\frac{\sqrt{a}}{2\sqrt{x}}-\frac{{{a}^{2}}}{2\sqrt{a}}{{x}^{-3/2}}\] \[\therefore \] \[f'(a)=\frac{\sqrt{a}}{2\sqrt{a}}-\frac{{{a}^{2}}}{2\sqrt{a}{{a}^{3/2}}}\] \[\Rightarrow \] \[f'(a)=\frac{1}{2}-\frac{{{a}^{2}}}{2{{a}^{2}}}=0\]
You need to login to perform this action.
You will be redirected in
3 sec
