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]

\(\displaystyle x\ is\ the\ variable.\)

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

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

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

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