Determine the Maximum Number of Turning Points of F $$f ( x ) = x ^ { 2 } ( x + 2 )$$

question 81

Short Answer

Determine the maximum number of turning points of f.
- $$f ( x ) = x ^ { 2 } ( x + 2 )$$
Answer: (a) For large values of $| x |$ , the graph of $f ( x )$ will resemble the graph of $y = x ^ { 3 }$ .
(b) $y$ -intercept: $( 0,0 )$ , $x$ -intercepts: $( 0,0 )$ and $( - 2,0 )$
(c) The graph of $f$ crosses the $x$ -axis at $( - 2,0 )$ and touches the $x$ -axis at $( 0,0 )$ .
(e) Local minimum at $( 0,0 )$ , Local maximum at $( - 1.33,1.19 )$
(f)

(g) Domain of f: all real numbers; range of f: all real numbers
(h) f is increasing on (-, -1.33) and (0, ); f is decreasing on (-1.33, 0)