Question

f(x)=mx+c & f(0)= f'(0)=1 so find f(2).

Answer 1

$f(x) = mx + c \\ \\ diff \\ \\ {f}^{1} (x) = m \\ \\ given \\ \\ f(0) = {f}^{1} (0) = 1 \\ \\ m(0) + c = 1 \\ \\ c = 1 \\ \\ also \\ \\ m = 1 \\ \\ therefore \\ \\ f(x) = x + 1 \\ \\ f (2)=2+1=3$

hope it helps

Answer 2

$f(x) = mx + c -------(1)\\ \\ diff \\ \\ {f}^{1} (x) = m \\ \\ given \\ \\ f(0) = {f}^{1} (0) = 1 \\ \\ m(0) + c = 1 \\ \\ c = 1 \\ \\ also \\ \\ m = 1 \\ \\ therefore \\ \\Substituting\: m=c=1\: in(1)\\\\ f(x) = x + 1 \\ \\now\\ \\ f (2)=2+1=3$

hope it helps