The graph of a function h (x) is shown to the right. Which of the following conclusions can be made about the derivative of h, h'(x)? A. h'(x)>0 when x = -3 B. h'(x)=0 when x = -2 C. h'(x)<0 when x = 2 D. both A and B are valid conclusions
The graph of a function h (x) is shown to the right. Which of the following conclusions can be made about the derivative of h, h'(x)? A. h'(x)>0 when x = -3 B. h'(x)=0 when x = -2 C. h'(x)<0 when x = 2 D. both A and B are valid conclusions
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The graph of a function h (x) is shown to the right. Which of the following conclusions can be made about the derivative of h, h'(x)?
A. h'(x)>0 when x = -3
B. h'(x)=0 when x = -2
C. h'(x)<0 when x = 2
D. both A and B are valid conclusions
Transcribed Image Text:The image contains a graph depicting a polynomial curve on a coordinate plane:
- **Axes**: The graph shows both the x-axis and y-axis marked in increments of 1, ranging from -5 to 5 on the x-axis and approximately -35 to 35 on the y-axis.
- **Curve**: The curve appears to graphically represent a polynomial function. It exhibits a wave-like pattern with the following characteristics:
- The function decreases sharply as it approaches x = -5, indicating the end behavior is downwards on the far left.
- Around x = -4.5, the curve has a local maximum before descending to a local minimum near x = -2.5.
- At x = -1.5, the curve crosses the x-axis and rises to another local maximum at approximately x = 0.5.
- The graph descends again, crossing the x-axis roughly at x = 2 and then rises steeply towards the right, indicating the end behavior is upwards on the far right.
This visual representation aids in understanding how polynomial functions can behave over different intervals and the nature of their turning points and intersections with the x-axis.
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