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## Main Question or Discussion Point

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

A) 0

B) 1

C) 2

D) n

E) 2n

- Thread starter European Sens
- Start date

- 19

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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

A) 0

B) 1

C) 2

D) n

E) 2n

- 1,631

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What do you think????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

And welcome to PF.

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I think its E.

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Why is that so?I think its E.

- 1,631

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f''(x) = 2-5cosx

0 = 2-5cosx

So whenever cosx = 2/5 there is a change in inflection. Then just figure out how many times that happens on [0,2pi*n]

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