find point of inflection of f(x) = sin^2(x) - sin(x)

[bcfr]

the original function is sin^2(x)-sin(x), the first derivative is 2sin(x)cos(x)-cos(x) and the 2nd derivative is -2sin^2(x)+sin(x)+2cos^2(x), please help me find the point of inflection

 

[mmm4444bot]

Hello BCfr:

Inflection points occur where the value of the second derivative changes sign.

(I did not verify your derivatives.)

In the future, please show some work or explain what you're thinking. You have a better chance of getting help at this web site when you show some initiative.

Also, please read the post titled "Read Before Posting", if you have not already done so.

Cheers,

~ Mark

 

[fasteddie65]

"the 2nd derivative is -2 sin^2 x + sin x + 2 cos^2 x"

I'm not sure why a previous post by galactus mentioned that sin^2 x + cos^2 x = 1.

Another hint would be that cos^2 x - sin^2 x = cos 2x.

So f"(x) = 2 cos 2x + sin x = 0
2(1 - 2 sin^2 x) + sin x = 0
2 - 4 sin^2 x + sin x = 0
0 = 4 sin^2 x - sin x - 2
Using Quadratic Formula, I get sin x = 0.84307033.. and sin x = -0.59307033...

Rather unpleasant solutions.

 

[galactus]

Yes, I misread. A booboo on my part.

My mind has been elsewhere lately.