Question

Show that every point on the curve y=b sin (x/a), where the curve meets the axes of x, is a point of inflextion.
Do i have to plainly show that x=0 is a POI or its asking for something else?

Answer 1

inflection tends to be a found by a second derivative; and tested for cavage

Answer 2

yeah i know that, but the language isnt very clear up there.

Answer 3

looks like: -b sin(x/a)/a^2 is the second derivative to me

Answer 4

yeah

Answer 5

since b=0 is trivial; it looks to be what x/a = any mutiple of pi

Answer 6

sorry didnt get that.

Answer 7

how to "show" it? i aint got a clue

Answer 8

sin(n*pi) = 0

so when x/a = n*pi we are at zero

Answer 9

yeah thats where i came, so is that the answer fianlly, x=0

Answer 10

x = a n*pi would seem to be the answer to me; but since n is an arbitrary integer then a*n would have to be an interger as well.

Answer 11

other than that; I got no idea what the "answer" might entail ....

Answer 12

umm, it says, where the curve meets the axes of x, so y=0 at that point, this only gives x=0.

Answer 13

inflection point is where the second derivative changes sign.
we know that
y=b sin (x/a)
crosses the x-axis when x/a is some multiple of 2pi
the 2nd derivative at these same points is -b sin(x/a)/a^2 = 0
also, if we go a dx distance below x/a and a little distance dx above x/a, the 2nd derivative changes sign. So we are at an inflection point.

Answer 14

That seems clear, understood, thank you phi and amistre for your time :)

Answer 15

*crosses the x-axis when x/a is some multiple of pi