**Educational Website Transcription:****Graph Analysis of a Derivative Function**The given graph represents the derivative \( f' \) of a continuous function \( f \) over the interval \( (0, 9) \). Use this graph to find the following:---**Graph Description:**The graph plots \( y = f'(x) \), showing a red curve that trends upwards and downwards across different intervals on the x-axis from 0 to 9. This curve crosses the y-axis and contains several peaks and valleys indicating changes in trends.---**Questions:****(a) Determine Intervals of Increase and Decrease for \( f \):**- **On what interval(s) is \( f \) increasing?** *(Enter your answer using interval notation.)* [Your Answer Here]- **On what interval(s) is \( f \) decreasing?** *(Enter your answer using interval notation.)* [Your Answer Here]**(b) Identify Local Maximum and Minimum Values for \( f \):**- **At what value(s) of \( x \) does \( f \) have a local maximum?** *(Enter your answers as a comma-separated list.)* \( x = \) [Your Answer Here]- **At what value(s) of \( x \) does \( f \) have a local minimum?** *(Enter your answers as a comma-separated list.)* \( x = \) [Your Answer Here]**(c) Recognize Concavity of \( f \):**- **On what interval(s) is \( f \) concave upward?** *(Enter your answer using interval notation.)* [Your Answer Here]- **On what interval(s) is \( f \) concave downward?** *(Enter your answer using interval notation.)* [Your Answer Here]**(d) Determine Points of Inflection for \( f \):**- **What are the \( x \)-coordinate(s) of the inflection point(s) of \( f \)?** *(Enter your answers as a comma-separated list.)* \( x = \) [Your Answer Here]---Use the graph to fill in your answers. The behavior of \( f' \) provides insights into the characteristics of the function \( f \), including its intervals of increase and

Name: **Educational Website Transcription:****Graph Analysis of a Derivativ
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: **Educational Website Transcription:****Graph Analysis of a Derivative Function**The given graph represents the derivative \( f' \) of a continuous function \( f \) over the interval \( (0, 9) \). Use this graph to find the following:---**Graph Desc

The graph of the function y= f1 (x) was given. (a) The function f is increasing if f1 (x) > 0 y > 0 (Since y=f1(x)) From the figure, observe that y>0 (positive y-axis) on the interval (1,6) and (8,9) Therefore, the function f is increasing on the intervals (1,6) and (8,9) The function f is decreasing if f1 (x)<0 y<0 (Sice y=f1(x)) From the figure, observe that y<0 (negative y-axis) on the interval (0,1) and(6,8) ------------------------------------------------------------------------ (b) From the figure, observe that the sign of the graph of y=f1(x) changes from negative to positive at x=1x=8 ⇒The graph of f is decrease to increase at x=1, x=8 ⇒f has local minimum at x=1,x=8 From the figure, observe that the sign of the graph of y=f1(x) changes from positive to negative at x=6 ⇒The graph of f is increase to decrease at x=6 ⇒f has local maximum at x=6(c) From the figure, observe that the graph of y=f1(x) is increase in the intervals (0,2),(3,5),(7,9) So,ddx(f1(x))>0 on the intervals. ⇒f''(x))>0 on these intervals ⇒f is concave up on (0,2),(3,5),(7,9) From the figure, observe that the graph of y=f1(x) is increase in the intervals (2,3),(5,7) So,ddx(f1(x))<0 on the intervals. ⇒f''(x))<0 on these intervals ⇒f is concave up down on (2,3),(5,7)