Question

The graph shows a solution y=G(x) of the differential equation (dy/dx)=g(x,y) with initial condition G(0)=0.
Using the graph as evidence, we observe that the pictured interval, G(x) is (increasing or decreasing)? and concave (up or down)?......

Answer 1

If we use Euler's method with \[x _{o}=0\] and step size \[\Delta x=c _{1}\] to obtain approximations \[A(c _{1}) and A(c _{2})\] which of the following are true?
\[A(c _{2})>G(c _{2})>G(c _{1})\]
\[A(c _{2})>G(c _{2})>A(c _{1})\]
\[A(c _{2})>G(c _{2})\]
\[G(c _{1})>A(c _{1})\]

Answer 2

@Needhelpstudying

Answer 3

@Ac3 Nincompoop was joking I don't know this stuff, sory

Answer 4

i'm mainly having a hard time with the 2nd part

Answer 5

who does?

Answer 6

@Lovelarap

Answer 7

@ganeshie8

Answer 8

oh, can't really help. this was different than what i expected. Try Mehek14... She might know.

Answer 9

@Mehek14

Answer 10

@Nnesha

Answer 11

@SithsAndGiggles

Answer 12

am i missing something... we can tell just by looking at G(x) that it is concave

Answer 13

if we move along the positive x direction, we can see that the slope is becoming more and more negative, thus the rate of change of slope is negative( i.e G(x) differentiated twice is negative)

Answer 14

if the slope is always decreasing along positive x,
then the euler approximation will be slightly higher than the actual solution G(x)

Answer 15

its decreasing and its concave up