# How do you sketch the graph #y=(2+sinx)^2# using the first and second derivatives from #0<=x<2pi#?

##### 1 Answer

See graph and explanation. x is in radian measure.

#### Explanation:

graph{ y= (2+sin x)^2 [-20, 20, -10, 10]} The period of y is

As 2 + sin x ranges from 1 to 3, y oscillates between 1 and 9.

y' = 2(2+sin x) cos x =0, when cos x = 0 and this x = an odd multiple

of

y''

+-2, +-3, ...#, giving points of inflexion (POI), upon the axial line y = 5.

I would like the readers to read my answer once again, looking at

the graph after reading every line in my answer.

The graph asked for is between x = 0 and x = 6.28, nearly, with ends

at (0, 4) and (6.28, 4).