For What Values Of $c$ Does the Curve Have Maximum and Minimum Points for the and Minimum

question 155

Multiple Choice

For what values of $c$ does the curve have maximum and minimum points for the given function $f ( x ) = c x ^ { 4 } - 5 x ^ { 2 } + 1 ?$
Select the correct answer.

• A) For \(c = 0 , f ( x ) = - 5 x ^ { 2 } + 1\), a parabola whose vertex \(( 0,2 )\), is the absolute maximum.
• For \(c > 0 , f ( x ) = c x ^ { 4 } - 5 x ^ { 2 } + 1\), opens downward with one minimum points.
• For \(c < 0\), the graph opens upward, and has an absolute maximum at \(x = 0\) and no local minimum.
• B) For \(c = 0 , f ( x ) = 5 x ^ { 2 } + 1\), a parabola whose vertex \(( 0,2 )\), is the absolute maximum.
• For \(c > 0 , f ( x ) = c x ^ { 4 } + 5 x ^ { 2 } + 1\), opens upward with two minimum points.
• For \(c < 0\), the graph opens downward, and has an absolute minimum at \(x = 0\) and no local minimum.
• C) For \(c = 0 , f ( x ) = 5 x ^ { 2 } + 1\), a parabola whose vertex \(( 0,3 )\), is the absolute maximum.
• For \(c > 0 , f ( x ) = c x ^ { 4 } - 5 x ^ { 2 } + 1\), opens upward with two minimum points.
• For \(c < 0\), the graph opens downward, and has an absolute minimum at \(x = 0\) and no local minimum.
• D) For \(c = 0 , f ( x ) = - 5 x ^ { 2 } + 1\), a parabola whose vertex \(( 0,1 )\), is the absolute maximum.
• For \(c > 0 , f ( x ) = c x ^ { 4 } - 5 x ^ { 2 } + 1\), opens upward with two minimum points.
• For \(c < 0\), the graph opens downward, and has an absolute maximum at \(x = 0\) and no local minimum.
• E) For \(c = 0 , f ( x ) = - 5 x ^ { 2 } + 1\), a parabola whose vertex \(( 0 , - 1 )\), is the absolute maximum.
• For \(c > 0 , f ( x ) = c x ^ { 4 } + 5 x ^ { 2 } - 1\), opens downward with two maximum points.
• For \(c < 0\), the graph opens upward, and has an absolute minimum at \(x = 0\).

Comprehend the requirements for a person to possess apparent authority.

Distinguish between actual express, implied, and apparent authority.

Identify the roles and powers of general and special agents.

Recognize the capacity requirements for principals and agents.

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Definitions:

PEM

Protein-Energy Malnutrition, a condition resulting from a diet lacking in adequate calories and protein.

Marasmus

A wasted, potentially lethal body condition caused by inadequate nutrition and characterized by painful thinness.

Essential Nutrients

Vital substances required for normal body functioning that must be obtained from the diet because they are not synthesized by the body in sufficient amounts.

Myelination

The process of forming a myelin sheath around the axons of neurons, which is critical for the proper functioning of the nervous system.