Question

4. The figure below shows the slope field for a differential equation
dydx=f(x)

Answer 1

4. The figure below shows the slope field for a differential equation
dydx=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

my guess for a is that x=2 and that would be the local minimum
my guess for b is that x=6 and that would be the local maximum
I have no idea on how to do c and d

Answer 3

fak you