Differentiation Question 302
Question: If $ y=\frac{a+b{x^{3/2}}}{{x^{5/4}}} $ and $ {y}’=0 $ at $ x=5 $ , then the ratio $ a:b $ is equal to
[AMU 2001]
Options:
A) $ \sqrt{5}:1 $
B) 5 : 2
C) 3 : 5
D) 1 : 2
Show Answer
Answer:
Correct Answer: A
Solution:
$ y=\frac{a+b{x^{3/2}}}{{x^{5/4}}} $
Therefore $ {y}’=\frac{\frac{3}{2}b{x^{7/4}}-\frac{5}{4}(a+b{x^{3/2}}){x^{1/4}}}{{x^{5/2}}} $
$ \because $ $ {y}’=0 $ at $ x=5 $
\ $ \frac{3}{2}b{x^{7/4}}-\frac{5}{4}(a+b{x^{3/2}}){x^{1/4}}=0 $ at $ x=5 $
Therefore $ 6b{x^{3/2}}-5(a+b{x^{3/2}})=0 $ at $ x=5 $
Therefore $ b{x^{3/2}}=5a $ at $ x=5 $
Therefore $ b{{(5)}^{3/2}}=5a $
Therefore $ \frac{a}{b}=\frac{{5^{3/2}}}{5} $
Therefore $ a:b=\sqrt{5}:1 $ .
BETA
