Question

If $f\left(x\right)=mx+c$ and if $f^{\prime }\left(0\right)=1,$ then find $f\left(2\right)$.

Answer 1

Consider the given function.

$f\left(x\right)=mx+c$

On differentiating w.r.t $x$, we get

$f^{\prime }\left(x\right)=m$

Since, $f^{\prime }\left(0\right)=1$

So,

$f^{\prime }\left(0\right)=m$

$m=1$

Now,

$f\left(x\right)=x+c$

On putting $x=2$, we get

$f\left(2\right)=2+c$

Hence, this is the answer.