Geometry of your personal function

(10 pts)

For this problem, you’re going to answer some questions concerning the first and second derivative of a graph build just for you. To get your graph, enter your name below. Once you have your graph, you can enter some points (just the x-coordinates) that you’d like plotted and automatically on the graph. You’ll want to choose those points to indicate maxima, minima, and inflection points. This should help you answer the questions below.

Once you have your labeled graph, you save and download it so that you can respond with the image of your labeled graph and the answers to the following:

1. Identify intervals on which f' > 0.
2. Identify intervals on which f' < 0.
3. Identify intervals on which f'' > 0.
4. Identify intervals on which f'' < 0.

1. f' > 0 for the intervals: (-2.2, -1) and (1,∞)
2. f' < 0 for the intervals: (-∞, -2.2) and (-1, 1)
3. f'' > 0 for the intervals: (-∞, -1.5) and (0, ∞)
4. f'' < 0 for the intervals: (-1.5, 0)

1. f' > 0 on (-2.5, -1.15) and (0.75, \infty)
2. f' < 0 on (-\infty, -2.5) and (-1.15, .75)
3. f'' > 0 on (-\infty, -1.9) and (-0.1, \infty)
4. f'' < 0 on (-1.9, -0.1)
   
   

   Moore Graph 9.3793×495 15.6 KB

1. f' > 0 on (-2.6, -1.4) and (0.5, \infty)
2. f' < 0 on (-\infty, -2.6) and (-1.4, 0.5)
3. f'' > 0 on (-\infty, -2.1) and (-0.37, \infty)
4. f'' <0 on (-2.1, -0.37)

graph (1)951×594 18.6 KB

1. f'>0 on intervals (-2.25,-1.25) and (.75, \infty)
2. f'<0 on intervals (-\infty,-2.25) and (-1.25,.75)
3. f''>0 on intervals (-\infty,-1.75) and (-.25,\infty)
4. f''<0 on interval (-1.75,-.25)

1. f' > 0 for (-2.37,-1.25) and (0.6, \infty)
2. f' < 0 for (- \infty,0.6) and (-1.25,0.6)
3. f'' > 0 for (- \infty,-2) and (-0.25, \infty)
4. f'' < 0 for (-2,-0.25)
   My graph:
   

1. (-2.3, -1.05), (0.95, \infty)
2. (-\infty, -2.3), (-1.05, 0.95)
3. (-\infty, -1.7), (0.1, \infty)
4. (-1.7, 0.1)

image1133×694 35.1 KB

1. f'>0 on (-2.25,-1.14) and (0.74,\infty).
2. f'<0 on (-\infty,-2.25) and (-1.14,0.74).
3. f''>0 on (-\infty,-1.7) and (-0.1,\infty).
   4.f''<0 on (-1.7,-0.1).

Here’s the labelled graph of my function:

graph1268×792 37.9 KB

1.f^{\prime }>0 on (-2.8, -1.5) and (0.45,\infty)
2.f^{\prime }<0 on (-\infty, -2.8) and (-1.5, 0.45)
3.f">0 on (-\infty, -2.15) and (-0.5, \infty)
4.f"<0 on (-2.15, -0.5)

graph872×545 16.7 KB

1. f’ > 0 on (-2.7, -1.2) and (1.8, infinity)
2. f’ < 0 on (-infinity, -2.7) and (-1.2, 1.8)
3. f" < 0 on (-infinity, -2.3) and (-0.4, infinity)
4. f" > 0 on (-2.3, -0.4)

graph1268×792 31.9 KB

1. f'(x) > 0 on (-2.5, -1.48) and (0.95, ∞),
2. f'(x) < 0 on (-∞, -2.5) and (-1.48, 0.95),
3. f''(x) > 0 on (-∞, -1.98) and (-0.2,∞ ), and
4. f''(x) < 0 on (-1.98, -0.2)

f’ > 0 (-2.31, -.98) and (.95, infinity)
f’ < 0 (-infinity, -2.31) and (-.98, .95)
f’’ > 0 (-infinity, -1.53) and (.19, infinity)
f’’ > 0 (-1.53,.19)

1. f'>0 when (-2.8, -1.5) (0.5, ∞)
2. f'<0 when (-∞, -2.8) (-1.5, 0.5)
3. f''>0 when (-∞, -2.1) (-0.4, ∞)
4. f''<0 when (-2.1, -0.4)

Here is the labeled graph of my function:

graph1268×792 43.7 KB

1. f^{\prime }>0 on \left(-2.6,-1\right) and \left(1.1,\infty \right)
2. f^{\prime }<0 on \left(-\infty ,-2.6\right) and \left(-1,1.1\right)
3. f^{''}>0 on \left(-\infty ,-1.9\right) and \left(0.1,\infty \right)
4. f^{''}<0 on \left(-1.9,0.1\right)

This is the graph of my function labeled:

graph1585×990 40.2 KB

I think my intervals are as follows:

1. f'>0

2. f^{\prime }<0

3. f''>0

4. f''<0

graph1268×792 30.4 KB

1. f' > 0 for the intervals: (-2.6, -1.28) and (0.89, \infty)
2. f' < 0 for the intervals: (-\infty, -2.6) and (-1.28, 0.89)
3. f'' > 0 for the intervals: (-\infty, -1.94) and (-0.1, \infty)
4. f'' < 0 for the intervals: (-1.94, -0.1)

@abjorkma,@dkey,@nevers,@cmarsha4,@sbindas

Please use the mathematical typesetting tools as described in this meta post.

graph (1)1268×792 29.2 KB

1. f' > 0 for the intervals: (0.5, -\infty) and (-2.6, -1.1)
2. f' < 0 for the intervals: (-\infty, -2.6) and (-1.1, 0.5)
3. f" > 0 for the intervals: (-\infty, -2) and (-0.25, \infty)
4. f" < 0 for the intervals: (-1.7, -0.4)

1. f '> 0\ for\ the\ intervals: (-2.2,-1) \ and \ (0.7,\infty)
2. f '< 0\ for\ the\ intervals: (-\infty,-2.2) \ and \ (-1.1,0.7)
3. f ''> 0\ for\ the\ intervals: (-\infty,-1.5) \ and \ (-0.1,\infty)
4. f ''< 0\ for\ the\ intervals: (-1.5,-0.1)