sketch the graph of a function that has the properties described below. (-2, -1), (-4, -4) and (-6, -7) are…
sketch the graph of a function that has the properties described below. (-2, -1), (-4, -4) and (-6, -7) are on the graph, f(-2)=0 and f(-6)=0; f(x)<0 for x > -4, f(-4)=0, f(x)>0 for x < -4. choose the correct graph below.
Answer
Explanation:
Step1: Analyze critical - points
The points $(-2, - 1),(-4,-4),(-6,-7)$ should be on the graph. Also, $f'(-2)=0$ and $f'(-6)=0$ mean there are horizontal tangents at $x = - 2$ and $x=-6$.
Step2: Analyze increasing and decreasing
Since $f'(x)<0$ for $x > - 4$, the function is decreasing for $x>-4$. Since $f'(x)>0$ for $x < - 4$, the function is increasing for $x < - 4$. And $f'(-4)=0$ is a local maximum.
Step3: Match with graphs
Graph B has points that could potentially be $(-2, - 1),(-4,-4),(-6,-7)$, horizontal tangents at appropriate $x$ - values, and is increasing for $x < - 4$ and decreasing for $x > - 4$.
Answer:
B