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.
-$$f ( x ) = x ^ { 3 } - 4 x + 3 ; [ 1,2 ]$$
A) $( 4,51 )$
B) $( - 1.15,6.08 )$
C) $( 0,3 )$
D) $( 1.15 , - 0.08 )$

Question

Quizplus · Accepted Answer

To find the turning points of the given polynomial function $f(x) = x^3 - 4x + 3$ within the domain interval [1,2], we first need to find its derivative, which is $f'(x) = 3x^2 - 4$. Setting the derivative equal to zero gives the critical points, which are potential turning points. Solving $3x^2 - 4 = 0$ gives $x = \pm \sqrt{\frac{4}{3}}$, which approximates to $x \approx \pm 1.15$. Only $x = 1.15$ falls within the given interval [1,2]. Substituting $x = 1.15$ into the original function gives a turning point at approximately $(1.15, -0.08)$, which is the closest to choice D when rounded to the nearest hundredth.

Use a Graphing Calculator to Find the Coordinates of the Turning