Thread: Inflection points

Find the inflection points for the function: f(x) = 8x + 3 - 2sinx on the interval from 0 to 3pi. Give x values only and round to three decimal places.


Another example of a problem that I understand in general, but the specific problem throws me off...I differentiated twice and got f''(x) = 2sinx

I set that to zero and got sinx = -2

I assume this means there is an inflection point at -2, correct? This should be simple but trig functions always throw me off.

Originally Posted by bobsanchez

I differentiated twice and got f''(x) = 2sinx

I set that to zero and got sinx = -2

I assume this means there is an inflection point at -2, correct? This should be simple but trig functions always throw me off.

No. If you're saying that $\displaystyle f''(x) = 2\sin\,x$, you set equal to 0:
$\displaystyle 2\sin\,x = 0$

... DIVIDE both sides by 2:
$\displaystyle \sin\,x = 0$

You're looking for angles whose sine is 0. You should have learned in trig that that occurs when $\displaystyle x = 0, \pi, 2\pi, (3\pi)$. (You say that the interval is from 0 to 3pi, but I don't know if you mean $\displaystyle [0, 3\pi]$ or $\displaystyle [0, 3\pi)$.)