Provide an Appropriate Response $f ( x ) = 4 x ^ { 3 } - 3 x - 4$

question 114

Essay

Provide an appropriate response.
-Explain why the following five statements ask for the same information.
(a) Find the roots of $f ( x ) = 4 x ^ { 3 } - 3 x - 4$ .
(b) Find the $x$ -coordinate of the points where the curve $y = 4 x ^ { 3 }$ crosses the line $y = 3 x + 4$ .
(c) Find all the values of $x$ for which $4 x ^ { 3 } - 3 x = 4$ .
(d) Find the $x$ -coordinates of the points where the cubic curve $y = 4 x ^ { 3 } - 3 x$ crosses the line $y = 4$ .
(e) Solve the equation $4 x ^ { 3 } - 3 x - 4 = 0$ .

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Definitions:

Framing

How information is presented affects how that information is perceived and influences decisions.

Subgoals

Smaller, achievable objectives set as steps that contribute towards the attainment of a larger goal.

Availability Heuristic

A mental shortcut that relies on immediate examples that come to a person's mind when evaluating a specific topic, concept, method, or decision.

Representativeness Heuristic

A cognitive shortcut that involves making judgments based on how much one entity represents, or is similar to, another entity.