Applications Of Derivatives Question 30
Question: If the sub-normal at any point on $ y={a^{1-n}}x^{n} $ is of constant length, then the value of n is
Options:
A) $ \frac{1}{4} $
B) 1
C) $ \frac{1}{3} $
D) $ \frac{1}{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ y={a^{1-n}}x^{n} $ or $ \frac{dy}{dx}={a^{1-n}}n{x^{n-1}} $
$ sub-normal=| y\frac{dy}{dx} |=| y{a^{1-n}}n{x^{n-1}} | $
$ =| {a^{1-n}}x^{n}{a^{1-n}}n{x^{n-1}} |=| {a^{2-2n}}{x^{2n-1}} | $ which is constant if $ 2n-1=0 $ or $ n=1/2 $ .
BETA
