Identify the function's local and absolute extreme values, if any, saying where they occur.
-$$f ( x ) = x ^ { 3 } + 2.5 x ^ { 2 } + 2 x - 3$$
A) local maximum at $x = - 1$; local minimum at $x = - \frac { 2 } { 3 }$
B) local maximum at $x = - \frac { 1 } { 3 }$; local minimum at $x = - 2$
C) local maximum at $x = 2$; local minimum at $x = \frac { 1 } { 3 }$
D) local maximum at $x = \frac { 2 } { 3 }$; local minimum at $x = 1$

Question

Quizplus · Accepted Answer

The derivative $f'(x) = 3x^2 + 5x + 2$ gives critical points at $x = -1$ and $x = -\frac{2}{3}$. Testing these points, $x = -1$ is a local maximum and $x = -\frac{2}{3}$ is a local minimum.

Identify the Function's Local and Absolute Extreme Values, If Any f(x)=x3+2.5x2+2x−3f ( x ) = x ^ { 3 } + 2.5 x ^ { 2 } + 2 x - 3f(x)=x3+2.5x2+2x−3

Identify the Function's Local and Absolute Extreme Values, If Any $f ( x ) = x ^ { 3 } + 2.5 x ^ { 2 } + 2 x - 3$