Applications Of Derivatives Question 346
Question: Function $ f(x)=x^{4}-\frac{x^{3}}{3} $ is
Options:
A) Increasing for $ x>,\frac{1}{4} $ and decreasing for $ x<\frac{1}{4} $
B) Increasing for every value of x
C) Decreasing for every value of x
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ f(x)=x^{4}-\frac{x^{3}}{3}\Rightarrow f’(x)=4x^{3}-x^{2} $
For increasing $ 4x^{3}-x^{2}>0=x^{2}(4x-1)>0 $
Therefore, the function is increasing for $ x>\frac{1}{4} $
Similarly decreasing for $ x<\frac{1}{4} $ .
BETA
