Find all points of inflection of the graph of the function $f ( x ) = 2 \sin 7 x + \sin 14 x \text { on }$ the interval . Round your answer to three decimal places wherever applicable.
A) $( 0.26,1.452 ) , ( 0.449,0 ) , ( 0.637 , - 1.452 )$
B) $( 0.282,1.11 ) , ( 0.669 , - 0.004 )$
C) $( 0.449,0 ) , ( 0.637 , - 1.452 )$
D) $( 0.26,1.452 ) , ( 0.449,0 ) , ( 0.659 , - 1.794 )$
E) $( 0.26,1.452 ) , ( 0.637 , - 1.452 )$

Question

Find all points of inflection of the graph of the function $f ( x ) = 2 \sin 7 x + \sin 14 x \text { on }$ the interval . Round your answer to three decimal places wherever applicable. 
A) $( 0.26,1.452 ) , ( 0.449,0 ) , ( 0.637 , - 1.452 )$
B) $( 0.282,1.11 ) , ( 0.669 , - 0.004 )$
C) $( 0.449,0 ) , ( 0.637 , - 1.452 )$
D) $( 0.26,1.452 ) , ( 0.449,0 ) , ( 0.659 , - 1.794 )$
E) $( 0.26,1.452 ) , ( 0.637 , - 1.452 )$

Quizplus · Accepted Answer

Points of inflection occur where the second derivative of the function changes sign, indicating a change in concavity. For the function $f(x) = 2\sin(7x) + \sin(14x)$, we find its second derivative and solve for $x$ where this derivative is zero or undefined, within the given interval. The points provided in option A, when substituted into the function and its derivatives, align with the criteria for inflection points, considering the periodic nature of the sine function and the coefficients involved.

Find All Points of Inflection of the Graph of the Function