help me

[r267747]

if f(x)=mx+c and if f(0)=f '(0)=1, what is f(2)
MY WORK:-
given f(x)=mx+c
.
. . f ' (x)=

d/dx(mx)+d/dx(c)
=m
Now from here i don't know how to find the value of f(2) i have tried but i failed to calculate the answer
so please help me
(answer is 3)

 

[soroban]

Hello, r267747!

$\displaystyle \text{Do you }really\text{ understand what }f(1)\text{ means?}$

$\displaystyle \text{If }f(x)\,=\,mx+c\,\text{ and if }f(0)=f '(0)=1,\:\text{ find }f(2)$

$\displaystyle \text{We are told that: }\,f(0) = 1$
. . $\displaystyle \text{So: }\;m(0) + c \:=\:1 \quad\Rightarrow\quad c \:=\:1$

$\displaystyle \text{We are told that: }\,f'(0) = 1$
$\displaystyle \text{We find that: }\,f'(x) = m$
. . $\displaystyle \text{So: }\:m \:=\:1$

$\displaystyle \text{Hence, the function is: }\:f(x) \:=\:x + 1$

Got it?

 

[chrisr]

$\displaystyle x\ is\ the\ variable.$

$\displaystyle To\ find\ f(2),\ you\ need\ to\ know\ m\ and\ c.$

$\displaystyle As\ things\ stand\ you\ can't\ calculate\ f(2)\ as\ you\ don't\ know\ m\ and\ c.$

$\displaystyle The\ two\ clues\ are\ designed\ to\ let\ you\ calculate\ m\ and\ c\,if\ you\ know\ how\ to\ differentiate.$

$\displaystyle Then\ you\ have\ the\ equation\ f(x)\ into\ which\ you\ can\ place\ x=2.$