question 2 (2 points) f(x)=x² + 6x + 4 round to the tenths (on decimal place!) relative maximums (if only…

question 2 (2 points) f(x)=x² + 6x + 4 round to the tenths (on decimal place!) relative maximums (if only one, put n/a in second blank):____ ____ relative minimas (if only one, put n/a in second blank):____ ____ intervals of increasing (if only one, put n/a in second blank):____u____ intervals of decreasing (if only one, put n/a in second blank):____u____ for infinity, use ∞ (you can copy and paste or find it in emojis and symbols). no spaces anywhere! blank 1: blank 2: blank 3: blank 4: blank 5: blank 6: blank 7: blank 8:

question 2 (2 points) f(x)=x² + 6x + 4 round to the tenths (on decimal place!) relative maximums (if only one, put n/a in second blank):____ ____ relative minimas (if only one, put n/a in second blank):____ ____ intervals of increasing (if only one, put n/a in second blank):____u____ intervals of decreasing (if only one, put n/a in second blank):____u____ for infinity, use ∞ (you can copy and paste or find it in emojis and symbols). no spaces anywhere! blank 1: blank 2: blank 3: blank 4: blank 5: blank 6: blank 7: blank 8:

Answer

Explanation:

Step1: Find the derivative

The derivative of $f(x)=x^{2}+6x + 4$ using the power - rule $(x^n)'=nx^{n - 1}$ is $f'(x)=2x+6$.

Step2: Find the critical points

Set $f'(x) = 0$. So, $2x+6=0$. Solving for $x$ gives $x=-3$.

Step3: Determine the second - derivative

The second - derivative $f''(x)=(2x + 6)'=2>0$. Since $f''(-3)=2>0$, the function has a relative minimum at $x = - 3$.

Step4: Find the relative minimum value

Substitute $x=-3$ into $f(x)$: $f(-3)=(-3)^{2}+6\times(-3)+4=9-18 + 4=-5$.

Step5: Determine intervals of increase and decrease

Set $f'(x)>0$ for increasing intervals: $2x+6>0$, which gives $x>-3$. So the increasing interval is $(-3,\infty)$. Set $f'(x)<0$ for decreasing intervals: $2x+6<0$, which gives $x<-3$. So the decreasing interval is $(-\infty,-3)$.

Answer:

Blank 1: N/A Blank 2: N/A Blank 3: -5 Blank 4: N/A Blank 5: (-3,∞) Blank 6: N/A Blank 7: (-∞,-3) Blank 8: N/A