Question

f(x) = 3 sin x + 3 cos x
0 ≤ x ≤ 2π. Find the interval in which f is concave up and concave down. Find the inflection points

Answer 1

First find derivative

Answer 2

3cosx-3sinx

Answer 3

to find inflection points, just take the second derivative, set it to zero and solve for x.

Answer 4

so the second derivative is -3sinx-3cos x

Answer 5

but how would i solve for that

Answer 6

factor out the -3?

Answer 7

set to 0 solve for x

Answer 8

to find the inflection points, you have to derive your function twice, and then you'll have to take 2 conditions.

1) f''(x) = 0
2) f''(x) = UND depends on the function ofcourse


when you set your derived function to zero, you'll get numbers, those are your x's and to find the y's to finish up your process , plug in the x you found in the original function, and with that, you'l have your inflection points ^_^

I hinted it for you, now give it a try :)

Answer 9

what about the concave up and down?

Answer 10

for that, you have to draw a table putting in the x, f''(x), and f in the first column like this :


x | (--) 0 (+)
___|________________________
f'' |
___|_________________________

f |

then you take negative values for x and plug them in the original function, if it gives you a negative answer then it's concaved down, and if it gives you a positive answer then it's concaved up. Same story goes when you take positive values for x~

after that, from the table, you'll be able to determine the intervals of concavity :)

Answer 11

This one is tricky. I think you have to plot sin x - cos x over your interveral 0 to 2 pi. You would get your max and min because it is a periodic function

Answer 12

oh, right, so you'll hav to list the x's on the x's row lol, you know -2pi -pi -pi/2 0 pi/2 ...e.tc :)

Answer 13

but since its between 0 and 2pi i do 0, pi/2, pi/3, pi?

Answer 14

Been a while since I did this. We need Lokisan or Xavier

Answer 15

You make a table x=0, f' (x) (or f''(x) which ever one=sinx - cos x. You evaluate over 4 intervals, you would get your max, min