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

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asked May 23, 2022 208k views

2 Answers

Unjuken · Answer 1 · 2022-05-30T11:07:33+0000

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 :)