Question

SLOPE FIELD QUESTION, NEED HELP

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

the slope field is

Answer 3

my guess for a is 2
for b is 6
im completely confused on c and d

Answer 4

The slope field is a visualization of the family of solutions. Notice that for this DE, the family of solutions is the same function differing only by a constant. What you need to do is extract the solution fro the slope field figure which intercepts the y-axis at -3.

Answer 5

why would you chose the figure which intercepts -3?

Answer 6

(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)

Answer 7

g(0) = -3

Answer 8

ah,

Answer 9

The red line in the picture I attached is a sketch of the function in the family of solutions that satisfies the requirement g(0) = -3

Answer 10

For part (d), you are considering our solution which we just found, and solving g(x) = 0. In other words we are finding the root(s) of the function we found. Do you understand?

Answer 11

thank you, your help helped me fix my mistake for b, and also helped me on c and d :)