Determine the maximum number of turning points of f.
-$$f ( x ) = ( x - 3 ) ^ { 2 } ( x + 5 ) ^ { 2 }$$
A) above the $x$-axis: $( - \infty , - 5 ) , ( 3 , \infty )$
below the x-axis: $( - 5,3 )$
B) above the x-axis: $( - 5,3 )$
below the $x$-axis: $( - \infty , - 5 ) , ( 3 , \infty )$
C) above the $x$-axis: $( - \infty , - 5 ) , ( - 5,3 ) , ( 3 , \infty )$
below the $x$-axis: no intervals
D) above the $x$-axis: no intervals
below the $x$-axis: $( - \infty , - 5 ) , ( - 5,3 ) , ( 3 , \infty )$

Question

Quizplus · Accepted Answer

The function $f(x) = (x - 3)^2(x + 5)^2$ is always non-negative because it is the square of two terms, meaning it cannot be below the x-axis. The function touches the x-axis at $x = 3$ and $x = -5$, but does not cross it, indicating that all intervals are above the x-axis.

Determine the Maximum Number of Turning Points of F f(x)=(x−3)2(x+5)2f ( x ) = ( x - 3 ) ^ { 2 } ( x + 5 ) ^ { 2 }f(x)=(x−3)2(x+5)2

Determine the Maximum Number of Turning Points of F $f ( x ) = ( x - 3 ) ^ { 2 } ( x + 5 ) ^ { 2 }$