Applications Of Derivatives Question 215
Question: Let $ f:(0,,+\infty )\to R $ and $ F(x)=\int_0^{x}{f(t),dt} $ . If $ F(x^{2})=x^{2}(1+x) $ , then $ f(4) $ equals
[IIT Screening 2001]
Options:
A) $ \frac{5}{4} $
B) 7
C) 4
D) 2
Show Answer
Answer:
Correct Answer: C
Solution:
$ x^{2}(1+x),=\int_0^{x^{2}}{,f(t),dt}. $
Differentiating w.r.t. x , $ 2x(1+x)+x^{2}=f(x^{2}),.,2x $
therefore $ f(x^{2})=1+x+\frac{x}{2},,x>0 $
Putting $ x=2, $
$ f(4)=1+2+\frac{2}{2}=4. $
BETA
