The derivative of h(x) is given by the function h '(x) = x + 2cosx. Use your calculator to determine the number of times the graph of h(x) changes concavity on the interval [0,4pi ]. Justify your answer using a complete sentence.

Question

anonymous · Answer

$$
h''(x) =1 - 2 \sin(x)
$$

anonymous · Answer

how did  you get it?

anonymous · Answer

what's the derivative of x?

anonymous · Answer

1

anonymous · Answer

What's the derivative of 2 cos(x)

anonymous · Answer

it is -2sin

anonymous · Answer

What is the derivative of h'(x)=x + 2 cos(x)

anonymous · Answer

o thats it then?

anonymous · Answer

yes. Now you have to see where 1 - 2 sin(x) is positive and when it is negative.

anonymous · Answer

it is positive when $  0\le x \le \frac \pi 6$

anonymous · Answer

how do you know?

anonymous · Answer

do you have a website  with more examples?

anonymous · Answer

It is also positive for  $ \frac {5 \pi} 6 \le x \le 2\pi $

anonymous · Answer

it is negative when $ \frac \pi 6 \le x \le \frac {5 \pi} 6$

anonymous · Answer

k thanks

anonymous · Answer

see my site http://saab.org

anonymous · Answer

in particular, visit http://moltest.missouri.edu/mucgi-bin/calculus.cgi

anonymous · Answer

So it changes twice then...right?