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)

Understand the functions and types of antibodies and their role in enhancing phagocytosis and initiating inflammation.

Recognize the concept of Tolerance and its significance in the immune response.

Describe the mechanisms through which cytotoxic T cells target and attack intracellular pathogens.

Identify the primary antibody produced in response to an antigen and its importance.

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Definitions:

Inductive Thinking

A cognitive process that encompasses deriving broad inferences from particular examples or situations.

Egocentrism

The inability to differentiate between one's own perspective and someone else's perspective.

Teenage Pregnancy

Pregnancy occurring in a female who is aged between 13 and 19.

Contraception Use

The practice of using preventive methods or devices to avoid pregnancy as a consequence of sexual intercourse.