Differentiation Question 313
Question: If $ f(x)=\sqrt{ax}+\frac{a^{2}}{\sqrt{ax}}, $ then $ f’(a)= $
[EAMCET 2002]
Options:
A) - 1
B) 1
C) 0
D) a
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x)=\sqrt{ax}+\frac{a^{2}}{\sqrt{ax}}, $ then
Therefore $ {f}’(x)=\frac{\sqrt{a}}{2\sqrt{x}}+\frac{a^{2}}{\sqrt{a}}( \frac{-1}{2}{x^{-3/2}} ) $
Therefore $ {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}}} $
Therefore $ {f}’(a)=\frac{1}{2}-\frac{a^{2}}{2a^{2}}=0 $ .
BETA
