question 3 (2 points) f(x)=−2x²−4x + 4 round to the tenths (on decimal place!) relative maximums (if only…

question 3 (2 points) f(x)=−2x²−4x + 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). blank 1: blank 2: blank 3: blank 4: blank 5: blank 6: blank 7: blank 8:

question 3 (2 points) f(x)=−2x²−4x + 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). 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 $f(x)=-2x^{2}-4x + 4$ using the power - rule $(x^n)'=nx^{n - 1}$ is $f'(x)=-4x-4$.

Step2: Find critical points

Set $f'(x) = 0$. So, $-4x-4=0$. Solving for $x$ gives $x=-1$.

Step3: Determine the second - derivative

The second - derivative $f''(x)=-4<0$. Since $f''(-1)<0$, the function has a relative maximum at $x = - 1$.

Step4: Find the relative maximum value

Substitute $x=-1$ into $f(x)$: $f(-1)=-2(-1)^{2}-4(-1)+4=-2 + 4+4=6$.

Step5: Determine intervals of increase and decrease

Choose a test point in the interval $(-\infty,-1)$, say $x=-2$. Then $f'(-2)=-4(-2)-4 = 4>0$, so the function is increasing on $(-\infty,-1)$. Choose a test point in the interval $(-1,\infty)$, say $x = 0$. Then $f'(0)=-4(0)-4=-4<0$, so the function is decreasing on $(-1,\infty)$.

Answer:

Blank 1: 6.0 Blank 2: N/A Blank 3: N/A Blank 4: N/A Blank 5: $(-\infty,-1)$ Blank 6: N/A Blank 7: $(-1,\infty)$ Blank 8: N/A