Question

Show that the derivative of a constant function on an interval is zero.

Answer 1

To prove :

If f(x) =c, for some constant c, then f'(x) = 0.

Proof :

Suppose f(x) = c for some constant c. Then the derivative of f(x) can be found as :

$f^{\prime }\left(x\right)=li{m}_{h\to 0}\frac{f(x+h)-f\left(x\right)}{h}$

$=li{m}_{h\to 0}\frac{c-c}{h}=0$