Identify Intervals on Which the Function Is Increasing, Decreasing, or Constant

question 68

Multiple Choice

Identify intervals on which the function is increasing, decreasing, or constant.
- $$f ( x ) = x ^ { 3 } - x ^ { 2 } + 2$$

• A) Increasing: \(( - \infty , 0 )\) and \(( 0.67 , \infty )\); decreasing: \(( 0,0.67 )\)
• B) Increasing: \(( 0,0.67 )\); decreasing: \(( - \infty , 0 )\) and \(( 0.67 , \infty )\)
• C) Increasing: \(( - \infty , - 2 )\) and \(( 2 , \infty )\); decreasing: \(( - 2,2 )\)
• D) Increasing: \(( - \infty , 0 )\) and \(( 0.67 , \infty )\); constant: \(( 0,0.67 )\)

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Definitions:

Proximate Causes

Immediate, underlying factors within an organism that explain "how" biological processes occur.

Diurnal Animals

Animals most active during the day (e.g., pigeons). Compare with crepuscular animals and nocturnal animals.

Navigation

Involves the use of cues to change direction when necessary in order to reach a specific destination; requires a sense of direction, called compass sense, and an awareness of location, called map sense.

Compass Sense

An ability observed in some animals, allowing them to navigate using Earth's magnetic field.