Question

4. The figure below shows the slope field for a differential equation . Let be the family of functions that are solutions of the differential equation.

Answer 1

4. The figure below shows the slope field for a differential equation \[\frac{ dy }{ dx } = f(x)\] . Let \[g(x)=\int\limits_{a}^{x}f(t)dt+C\] be the family of functions that are solutions of the differential equation.

(a) Determine to the nearest integer the value of x for which all of the members of the family of g(x) will have a relative minimum value. Explain how you know.



(b) Determine to the nearest integer the value of x for which all of the members of the family of g(x) will have a relative maximum value. Explain how you know.



(c) On the figure below sketch the member of the family of g(x) for which g(0) = –3. (You may copy the figure on to a separate paper and fax to your instructor or you may scan it and attach it to your assignment)



(d) For the function sketched in part (c), determine the solution(s) of g(x)=0 to the nearest integer.

Answer 2

for part a :
Notice that the slope is 0 at \(x=2\), increasing as u move right
=> a local minimum

Answer 3

use similar reasoning for part b

Answer 4

im sorry for being oblivious, but i don't understand, how did u find that the slope is 0 at x=2

Answer 5

you're given a slope field

Answer 6

each segment is a tangent drawn at that point

Answer 7

at x = 2, the slope segment is flat horizontal, right ?