Find the point of inflection of the graph of the function $f ( x ) = 2 \sin \frac { x } { 7 }$ on the interval $[ 0,14 \pi ]$
A) $( 0,0 )$
B) $( 2 \pi , 0 )$
C) $( 8 \pi , 0 )$
D) $( 7 \pi , 0 )$
E) $( 7 \pi , 2 )$

Question

Quizplus · Accepted Answer

The second derivative of the function is $f''(x) = -\frac{2}{49} \cos \frac{x}{7}$. The second derivative is zero when $\cos \frac{x}{7} = 0$, which occurs when $\frac{x}{7} = \frac{\pi}{2} + n\pi$ for some integer $n$. Solving for $x$, we get $x = 7\pi + 14n\pi$. The only value of $x$ in the interval $[0, 14\pi]$ that satisfies this equation is $x = 7\pi$. Therefore, the point of inflection is $(7\pi, 0)$.

Find the Point of Inflection of the Graph of the Function