Use a graphing utility to graph the function and approximate (to two decimal places)any relative minimum or relative maximum values. $$f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 2 x + 3$$
A)relative maximum: (2.58,0.39) relative minimum: (7.27,-1.72)
B)relative maximum: (0.39,2.58) relative minimum: (-1.72,7.27)
C)relative maximum: (-1.72,7.27) relative minimum: (0.39,2.58)
D)relative maximum: (7.27,-1.72) relative minimum: (2.58,0.39)
E)relative maximum: (2.58,28.33) relative minimum: (7.27,478.41)

Question

Quizplus · Accepted Answer

To find the relative maximum and minimum of the function $f(x) = x^3 + 2x^2 - 2x + 3$, we first find its derivative: $f'(x) = 3x^2 + 4x - 2$. Setting $f'(x) = 0$ gives the critical points, which are approximately $x = -1.72$ and $x = 0.39$. Evaluating $f(x)$ at these points gives the y-values for the relative maximum and minimum. The correct coordinates are $(-1.72, 7.27)$ for the relative maximum and $(0.39, 2.58)$ for the relative minimum, matching choice C.

Use a Graphing Utility to Graph the Function and Approximate f(x)=x3+2x2−2x+3f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 2 x + 3f(x)=x3+2x2−2x+3

Use a Graphing Utility to Graph the Function and Approximate $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 2 x + 3$