If n is a positive integer, how many times does the function f(x) = x^2 + 5cosx change concavity in the interval 0 <= x <= 2*pi*n?

A) 0

B) 1

C) 2

D) n

E) 2n

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- Mar 10th 2008, 09:05 PMDINOCALC09concavity
If n is a positive integer, how many times does the function f(x) = x^2 + 5cosx change concavity in the interval 0 <= x <= 2*pi*n?

A) 0

B) 1

C) 2

D) n

E) 2n - Mar 11th 2008, 11:11 AMtopsquark
- Mar 12th 2008, 07:48 PMDINOCALC09
1st derivative = 2x - 5sinx

2nd derivative = 2 - 5cosx

set 2nd derivative = 0

so:

2 - 5cosx = 0

cosx = -2 / -5

x = arccos(-2/5)

This is only satisfied once?

So the answer should be (B) ? - Mar 13th 2008, 09:09 AMDINOCALC09
or is the answer E?

thats what my friend got. we still lack a definent answer though. - Mar 13th 2008, 04:43 PMmr fantastic
- Mar 13th 2008, 05:30 PMDINOCALC09
i believe i did that up above... not sure if i did it right or not, but yeah =/

- Mar 13th 2008, 06:51 PMmr fantastic
- Mar 13th 2008, 06:56 PMmr fantastic