Question

Find the derivative of $f\left(x\right)=3$ at $x=0$ and at $x=3$.

Answer 1

Given $f\left(x\right)=3$
We know that $f^{\prime }\left(x\right)=\underset{h\to 0}{lim}\frac{f(x+h)-f\left(x\right)}{h}$
$\Rightarrow f^{\prime }\left(x\right)=\underset{h\to 0}{lim}\frac{3-3}{h}$
$\Rightarrow f^{\prime }\left(x\right)=\underset{h\to 0}{lim}\frac{0}{h}$
$\Rightarrow f^{\prime }\left(x\right)=0$
Thus, $f^{\prime }\left(x\right)=0$
Putting $x=0$
$\Rightarrow f^{\prime }\left(0\right)=0$
Putting $x=3$
$\Rightarrow f^{\prime }\left(3\right)=0$
Hence, derivative $f\left(x\right)$ at $x=0$ and at $x=3$ is $0$.