find the intervals on which ( f(x) ) is increasing, the intervals on which ( f(x) ) is decreasing, and the…

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

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

Answer

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:

$3x^{2}+7$