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.
-$$f ( x ) = x ^ { 3 } - 2 x + 3 ; [ 0,1 ]$$
A) $( - 0.82,4.09 )$
B) $( 2,7 )$
C) $( 0,3 )$
D) $( 0.82,1.91 )$

Question

Quizplus · Accepted Answer

To find the turning points of the given polynomial function $f(x) = x^3 - 2x + 3$ within the domain interval $[0,1]$, we first calculate its derivative to find the critical points: $f'(x) = 3x^2 - 2$. Setting the derivative equal to zero gives the critical points, which, after solving, includes $x = \sqrt{\frac{2}{3}}$, approximately $0.82$. Evaluating $f(0.82)$ gives approximately $1.91$, thus the turning point in the given interval is $(0.82, 1.91)$.

Use a Graphing Calculator to Find the Coordinates of the Turning