Question

How do I use the limit definition of derivative to find `f'(x)` for `f(x)=c` ?

Answer 1

`f(x)=c` is a constant function, so its value stays the same regardless of the x-value. In particular, `f(x+h)=c`.

By the definition of the derivative,

`f'(x)=lim_{h to 0}{f(x+h)-f(x)}/h`

`=lim_{h to 0}{c-c}/{h}`

`=lim_{h to 0}0`

`=0`