Determine the maximum number of turning points of f.
-$$f ( x ) = ( x - 4 ) ^ { 3 }$$
A) above the $x$-axis: $( 4 , \infty )$
below the $x$-axis: $( - \infty , 4 )$
B) above the $x$-axis: $( - \infty , 4 ) , ( 4 , \infty )$
below the $x$-axis: no intervals
C) above the x-axis: no intervals
below the $x$-axis: $( - \infty , 4 ) , ( 4 , \infty )$
D) above the $x$-axis: $( - \infty , 4 )$
below the $x$-axis: $( 4 , \infty )$

Question

Quizplus · Accepted Answer

The function $f(x) = (x - 4)^3$ is a cubic function with one real root at $x = 4$. Since it is an odd-degree polynomial, it will extend from the lower left quadrant to the upper right quadrant of the Cartesian plane, meaning it will be below the $x$-axis when $x < 4$ and above the $x$-axis when $x > 4$. There are no turning points because the graph is monotonic, continuously increasing or decreasing without any bends.

Determine the Maximum Number of Turning Points of F f(x)=(x−4)3f ( x ) = ( x - 4 ) ^ { 3 }f(x)=(x−4)3

Determine the Maximum Number of Turning Points of F $f ( x ) = ( x - 4 ) ^ { 3 }$