Question

find the intervals on which ( f(x) ) is increasing, the intervals on which ( f(x) ) is decreasing, and the local extrema.
( f(x)=x^{3}+7x - 8 )
find the derivative ( f(x) )
( f(x)=square )

Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $y = x^n$, then $y^\prime=nx^{n - 1}$. Given $f(x)=x^{3}+7x - 8$.
The derivative of $x^{3}$ is $3x^{2}$ (since $n = 3$), the derivative of $7x$ is $7$ (since for $y = 7x^1$, $y^\prime=7\times1\times x^{1 - 1}=7$) and the derivative of a constant $- 8$ is $0$.
So, $f^\prime(x)=3x^{2}+7$.

Answer:

$3x^{2}+7$