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.
-$$f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 37 x - 90 ; [ 2,3 ]$$
A) $( 0,10 )$
B) $( 3.50 , - 103.12 )$
C) $( 2.04 , - 132.02 )$
D) $( - 6.04,132.02 )$

Question

Quizplus · Accepted Answer

To find the turning points of the given polynomial function $f(x) = x^3 + 6x^2 - 37x - 90$ within the domain interval [2,3], one would typically use a graphing calculator to plot the function and visually identify the turning points within the specified interval. The correct answer, (C) $(2.04, -132.02)$, is the turning point that falls within the given domain interval, as determined by the graphing calculator's output. This point is where the derivative of the function changes sign, indicating a local maximum or minimum within the interval.

Use a Graphing Calculator to Find the Coordinates of the Turning