Find the point(s) of inflection of the graph of $f ( x ) = \cos ^ { - 1 } 7 x$.
A) $( 1,0 ) , \left( 0 , \frac { \pi } { 2 } \right)$, and $\left( 0 , \frac { \pi } { 7 } \right)$
B) $( 1,0 )$
C) $\left( 0 , \frac { \pi } { 7 } \right)$
D) $\left( 0 , \frac { \pi } { 2 } \right)$

Question

Quizplus · Accepted Answer

Points of inflection occur where the second derivative changes sign, indicating a change in concavity. However, the function $f(x) = \cos^{-1}(7x)$ does not have points of inflection in the traditional sense because it is the inverse cosine function scaled by a factor of 7 in the argument, which does not lead to inflection points as defined in calculus. The choices given seem to misunderstand the nature of inflection points or the function itself. The closest valid interpretation might be considering the domain and range of the function, but none of the points listed correspond to inflection points of the given function. The correct answer should reflect a misunderstanding or a trick question, but given the options and typical calculus principles, none of the points listed are valid inflection points for the function described. My explanation was based on a standard calculus approach, but it seems there was a mistake in interpreting the question's intent or the properties of the inverse cosine function.

Find the Point(s) of Inflection of the Graph Of f(x)=cos⁡−17xf ( x ) = \cos ^ { - 1 } 7 xf(x)=cos−17x

Find the Point(s) of Inflection of the Graph Of $f ( x ) = \cos ^ { - 1 } 7 x$