A) f is a linear function
B) \[f\left( x \right)=3x+{{x}^{2}}\]
C) \[f\left( x \right)=3x+\frac{{{x}^{2}}}{2}\]
D) None of these
Correct Answer: C
Solution :
\[f'\left( x \right)=\underset{h\to 0}{\mathop{\operatorname{Lim}}}\,\frac{f\left( x+h \right)-f\left( x \right)}{h}\] |
\[=\underset{h\to 0}{\mathop{Lim}}\,\frac{f\left( x \right)+f\left( h \right)+xh-f\left( x \right)}{h}\] |
\[=\underset{h\to }{\mathop{Lim}}\,\frac{1}{h}f\left( h \right)+x=3+x\] |
Integrating we get \[f\left( x \right)=3x+\frac{{{x}^{2}}}{2}+\text{ }c\] |
Putting \[x=y=0\]in the given equation, we get |
\[f(0)=0\Rightarrow c=0\therefore f(x)=3x+\frac{{{x}^{2}}}{2}\] |
You need to login to perform this action.
You will be redirected in
3 sec