Applications Of Derivatives Question 398
Question: Let $ f,(x)=1+2x^{2}+2^{2}x^{4}+…..+2^{10}x^{20} $ , then $ f(x) $ has
[AMU 2005]
Options:
A) More than one minimum
B) Exactly one minimum
C) At least one maximum
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ f(x)=1+2x^{2}+2^{2}x^{4}+2^{3}x^{6}+{{…2}^{10}}x^{20} $
$ {f}’(x)=x(4+{{4.2}^{2}}x^{2}+….+{{20.2}^{10}}x^{18}) $
$ \therefore $ $ {f}’(x)=0 $
therefore $ x=0 $ only. Also $ {f}’’(0)>0 $ .
BETA
