Question

Let f(x)=x^3-6x+3 i. find the domain of the function and f’(x) in the domain.​

Answer 1

Explanation:

`thank \: you`

Answer 2

Domain of a any cubic function
`f(x)=ax^3+bx^2+cx+d` is defined to be always
`\mathbb{R}`.

The derivative with respect to x of your cubic function is,

`(d)/(dx)f(x)=f'(x)`

to find the derivative of a polynomial function, simply take a derivative of each factor and sum them up,

`(d)/(dx)x^3=3x^2` by the rule
`(d)/(dx)x^m=mx^(m-1)` where
`m\in\mathbb{R}`

`(d)/(dx)-6x=-6`

`(d)/(dx)3=0`

So the derivative is,

`f'(x)=3x^2-6`

both derivative and the original function have equal domain.

Hope this helps :)