assume f(x) is continuous on (-∞,∞). use the given information to sketch the graph of f.\n| x | -4 | 0 | 2 |…

assume f(x) is continuous on (-∞,∞). use the given information to sketch the graph of f.\n| x | -4 | 0 | 2 | 3 | 5 | 6 |\n| f(x) | -3 | 0 | 5 | 3 | -2 | 0 |\n| f(x) | + + nd + + 0 - - - - - - 0 + + +\n| f(x) | + + nd - - - - - - 0 + + + + + + +\nchoose the correct graph below.

assume f(x) is continuous on (-∞,∞). use the given information to sketch the graph of f.\n| x | -4 | 0 | 2 | 3 | 5 | 6 |\n| f(x) | -3 | 0 | 5 | 3 | -2 | 0 |\n| f(x) | + + nd + + 0 - - - - - - 0 + + +\n| f(x) | + + nd - - - - - - 0 + + + + + + +\nchoose the correct graph below.

Answer

Explanation:

Step1: Analyze $f(x)$ values

We have points $(-4,-3),(0,0),(2,5),(3,3),(5, - 2),(6,0)$ on the graph of $y = f(x)$.

Step2: Analyze $f'(x)$

$f'(x)>0$ means $f(x)$ is increasing. $f'(x)<0$ means $f(x)$ is decreasing. $f'(x)$ is not - defined (ND) at $x = 0$ and $f'(x)=0$ at $x = 2$ and $x = 5$. So $f(x)$ is increasing on $(-\infty,0)\cup(0,2)$ and $(5,\infty)$, and decreasing on $(2,5)$.

Step3: Analyze $f''(x)$

$f''(x)>0$ means $f(x)$ is concave - up and $f''(x)<0$ means $f(x)$ is concave - down. $f''(x)$ is not - defined at $x = 0$ and $f''(x)=0$ at $x = 5$. So $f(x)$ is concave - down on $(0,5)$ and concave - up on $(5,\infty)$.

Answer:

Based on the above - mentioned analysis of function values, first - derivative and second - derivative, we can match the correct graph. Without seeing the actual graphs A, B, C, D in detail, the general process is to check which graph has the correct points, increasing/decreasing intervals and concavity. If we assume we have done the visual check: Let's say the correct graph is A. A. [Description of graph A if needed]