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.
-$$f ( x ) = - x ^ { 4 } + 29 x ^ { 2 } - 100 ; [ 3,4 ]$$
A) $( 3.81,110.25 )$
B) $( 5,887.50 )$
C) $( 0,100 )$
D) $( - 4,110.25 )$

Question

Quizplus · Accepted Answer

The turning point within the domain interval [3,4] can be found using a graphing calculator to plot the function and identify local maxima or minima within this range. The function $f(x) = -x^4 + 29x^2 - 100$ is a quartic polynomial, and its graph will show turning points where the derivative equals zero. The coordinates $(3.81, 110.25)$ fall within the given interval and represent a turning point of the function, as determined by graphing or calculus methods. Other options are either outside the specified interval or do not correspond to turning points of the function within the given domain.

Use a Graphing Calculator to Find the Coordinates of the Turning