Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the
indicated domain interval. Give answers to the nearest hundredth.
-$$f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - 21 x - 108 ; [ 1,2 ]$$
A) $( 0,12 )$
B) $( 3.50 , - 40.62 )$
C) $( - 6.42,91.94 )$
D) $( 1.09 , - 120.09 )$

Question

Quizplus · Accepted Answer

To find the turning points of the given polynomial function $f(x) = x^3 + 8x^2 - 21x - 108$ within the interval $[1,2]$, we first need to find its derivative, which is $f'(x) = 3x^2 + 16x - 21$. Solving $f'(x) = 0$ gives the critical points, which are potential turning points. However, without solving it explicitly here, we rely on the use of a graphing calculator as instructed. By graphing $f(x)$ and examining it within the interval $[1,2]$, we identify the turning point's coordinates. Among the given options, only $(1.09, -120.09)$ falls within this interval, making it the correct choice. The other options are either outside the interval or not turning points of the function within the specified domain.

Use a Graphing Calculator to Find the Coordinates of the Turning