Integral Calculus Question 155
Question: If $ f’(x)=x^{2}+5 $ and $ f(0)=-1 $ , then $ f(x)= $
Options:
A) $ x^{3}+5x-1 $
B) $ x^{3}+5x+1 $
C) $ \frac{1}{3}x^{3}+5x-1 $
D) $ \frac{1}{3}x^{3}+5x+1 $
Show Answer
Answer:
Correct Answer: C
Solution:
Given that $ {f}’(x)=x^{2}+5 $ and $ f(0)=-1 $
Þ $ f(x)=\frac{x^{3}}{3}+5x+c $ . If $ x=0, $ then $ f(0)=c $
Þ $ c=-1 $ . Hence $ f(x)=\frac{x^{3}}{3}+5x-1. $
BETA
