Question

**AP CALCULUS Please Help Me(:**
given the function defined by y=x+sinx for all x such that -pie/2<(or equal to)x<(or equal to) 3pie/2
a) find the coordinate of all maximum and minimum points on the given interval.
b)find the coordinates of all points of inflection on the given interval.
c)sketch the graph of the function.
How do I start this off? With finding f prime and finding the critical values? same with the derivative of f prime ? thanks so much you guys(:

Answer 1

First, take the derivative of the function. What do you get?

Answer 2

hey (: thanks so much for responding. A

Answer 3

and i believe it is y'=1+cosx

Answer 4

That's right. Now find f''.
Or y'', if you like.

Answer 5

okay so i think y''=-sinx? do I need to equal both f prime and the derivative of f prime to zero to make a sign graph in order to find the maxima and minima ?

Answer 6

Bingo.

Now for a you want to set y' to 0 to see the critical points in the domain.

Answer 7

and that will equal (y') cosx=-1

Answer 8

Yes. At which angles in the domain is that true?

Answer 9

and this is the point on where I don't know what todo :( .

Answer 10

do I need to plug in a value and if yes, which ones?

Answer 11

Well, you've got to know where the cosine is -1.

https://www.khanacademy.org/math/trigonometry/trig-function-graphs/trig_graphs_tutorial/v/we-graph-of-cosine-function

Answer 12

at the relative max or min: \(y' = 0\) and \(y'' \ne 0\)

Answer 13

\[y'=0\\ \implies1+\cos x=0\\ \implies\cos x=-1\]

when is cosine -1 ?

Answer 14

oh okay so I have plug that in in the original function?