$$f ( x ) = \frac { 1 } { 3 } x ^ { 2 } \left( x ^ { 2 } - 5 \right) ( x - 3 )$$

question 17

Multiple Choice

$$f ( x ) = \frac { 1 } { 3 } x ^ { 2 } \left( x ^ { 2 } - 5 \right) ( x - 3 )$$

• A) 0 , multiplicity 2 , touches \(x\)-axis;
• 3 , multiplicity 1 , crosses \(x\)-axis;
• \(\sqrt { 5 }\), multiplicity 1 , crosses \(x\)-axis
• \(- \sqrt { 5 }\), multiplicity 1 , crosses \(x\)-axis
• B) 0 , multiplicity 2 , crosses \(x\)-axis;
• 3 , multiplicity 1 , touches \(x\)-axis;
• \(\sqrt { 5 }\), multiplicity 1 , touches \(x\)-axis;
• \(- \sqrt { 5 }\), multiplicity 1 , touches \(x\)-axis
• C) 0 , multiplicity 2, crosses x-axis;
• 3 , multiplicity 1 , touches \(x\)-axis
• D) 0 , multiplicity 2 , touches \(x\)-axis;
• 3 , multiplicity 1 , crosses \(x\)-axis

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Definitions:

Loves

An intense feeling of deep affection towards a person, place, thing, or concept.

Existential Generalization

A principle in logic where from a specific case, one infers the existence of cases or a generic form.

Quantifier Negation

The process of negating the quantifiers in logical expressions, effectively altering the scope and meaning of the statement.

Universal Generalization

A principle in logic and mathematics that allows for the formulation of a general statement from the observation of particular instances.