Applications Of Derivatives Question 355
Question: The minimum value of $ ( x^{2}+\frac{250}{x} ) $ is
[Kurukshetra CEE 2002]
Options:
A) 75
B) 50
C) 25
D) 55
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ y=f(x)=( x^{2}+\frac{250}{x} ) $ , $ \frac{dy}{dx}={f}’(x)=2x-\frac{250}{x^{2}} $
Put $ {f}’(x)=0 $
therefore $ 2x^{3}-250=0 $
therefore $ x^{3}=125 $
therefore $ x=5 $
Again, $ \frac{d^{2}y}{dx^{2}}={f}’’(x)=2+\frac{500}{x^{3}} $ .Now $ {f}’’(5)=2+\frac{500}{125}>0 $
Hence at $ x=5 $ . The function will be minimum. Minimum value $ f(5)=25+50=75 $ .
BETA
