Can you help me with this question? Based on the information in the photo does graph a) b) c) or d) match? ### Possible Graph of a Function \( f(x) \)Given the information below, determine which of the following is a possible graph of \( f(x) \):#### Conditions:- **The domain of \( f(x) \):** \( (-\infty, \infty) \).- **\( f'(x) > 0 \):** on \( (-\infty, -1) \cup (3, \infty) \).- **\( f'(x) < 0 \):** on \( (-1, 3) \).- **\( f''(x) < 0 \):** on \( (-\infty, 1) \).- **\( f''(x) > 0 \):** on \( (1, \infty) \).#### Graphs:##### (a)- **Description**: The graph starts from the top left, decreasing until \( x = -2 \). It then increases to a local maximum at \( x = 0 \), decreases again to a minimum at \( x = 2 \), and finally increases.##### (b)- **Description**: The graph begins at a high point on the left, decreases to a minimum around \( x = -3 \), increases to a local maximum at \( x = 1 \), then decreases.Based on the conditions:1. **\( f'(x) > 0 \):** Increasing intervals should match the increasing parts of the graphs.2. **\( f'(x) < 0 \):** Decreasing intervals should match the decreasing sections.3. **\( f''(x) < 0 \):** Concave down sections align with decreasing slope of \( f'(x) \).4. **\( f''(x) > 0 \):** Concave up sections align with increasing slope of \( f'(x) \).**Note**: Use these criteria to determine which graph satisfies all the conditions for \( f(x) \). The image contains two graphs labeled (c) and (d).### Graph (c):- The graph represents a curve labeled \( f(x) \).- The x-axis ranges from \(-4\) to \(5\), with a scale marker at \(5\).- The y-axis ranges from \(-30\) to \(20\).- The curve starts from the top left, descends steeply to a minimum point near \((0, -25)\), rises again to a local maximum near \((3, 10)\), and then dips downwards towards the bottom right.### Graph (d):- The graph represents a curve labeled \( f(x) \).- The x-axis ranges from \(-4\) to \(5\), with a scale marker at \(5\).- The y-axis ranges from \(-20\) to \(30\).- The curve starts from the bottom left, rises steeply to a maximum near \((0, 30)\), descends to a minimum near \((2.5, 0)\), and then rises towards the top right.Both graphs are plotted on a grid, facilitating an easy reading of values and trends of the function \( f(x) \).

Name: Can you help me with this question? Based on the information in the ph
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Can you help me with this question? Based on the information in the photo does graph a) b) c) or d) match? ### Possible Graph of a Function \( f(x) \)Given the information below, determine which of the following is a possible graph of \( f(x) \):####