Given $f(x)=x^{2}+6 x$ . (a) Find the intervals on which f is increasing or decreasing.
(b) Find the relative maxima and relative minima of f.
A) (a) Increasing on $(-3, \infty)$ ,
Decreasing on $(-\infty,-3)$
(b) Rel. min. $f(-3)=-9$
B) (a) Increasing on $(-\infty,-3)$ ,
Decreasing on $(-3, \infty)$
(b) Rel. max. $f(-3)=-9$
C) (a) Increasing on $(-6, \infty)$ ,
Decreasing on $(-\infty,-6)$
(b) Rel. min. $f(-6)=0$
D) (a) Increasing on $(-\infty,-6)$ ,
Decreasing on $(-6, \infty)$
(b) Rel. max. $f(-6)=0$

Question

Quizplus · Accepted Answer

The derivative of f is $f'(x)=2x+6$. Since $f'(x)>0$ for $x>-3$, f is increasing on $(-3, \infty)$. Since $f'(x)<0$ for $x<-3$, f is decreasing on $(-\infty,-3)$. The relative minimum of f occurs at $x=-3$, where $f(-3)=-9$.

Given f(x)=x2+6xf(x)=x^{2}+6 xf(x)=x2+6x (A) Find the Intervals on Which F Is Increasing

Given $f(x)=x^{2}+6 x$ (A) Find the Intervals on Which F Is Increasing