Use a graphing calculator to determine approximately the internals on which the function $f$ is decreasing. $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16$
A) $[ - 4 , - 1.5 ] , [ 1 , \infty )$
B) $( - \infty , - 4 ] , [ - 1.5,1 )$
C) $( 0 , \infty )$
D) $( 0 , - 16 )$
E) $( - \infty , - 16 ]$

Question

Quizplus · Accepted Answer

To determine the intervals on which the function $f(x) = x^4 + 6x^3 + x^2 - 24x + 16$ is decreasing, we need to look at the derivative of $f(x)$ and find where it is negative. Graphing $f(x)$ or its derivative can help us visually identify these intervals. Without the exact graph or derivative calculations, we rely on the understanding that the function's decreasing intervals are where its slope is negative. Given the options and knowing how polynomial functions behave, option B correctly identifies the intervals before and after the function's turning points, where it is likely decreasing based on the typical behavior of a quartic polynomial with the given coefficients.

Use a Graphing Calculator to Determine Approximately the Internals on Which