$\text { Find the open interval(s) on which } f ( x ) = - 2 x ^ { 2 } + 12 x + 8 \text { is increasing or decreasing. }$

question 57

Multiple Choice

$\text { Find the open interval(s) on which } f ( x ) = - 2 x ^ { 2 } + 12 x + 8 \text { is increasing or decreasing. }$

• A) increasing on \(( - \infty , 6 )\); decreasing on \(( 6 , \infty )\)
• B) increasing on \(( - \infty , 16 )\); decreasing on \(( 16 , \infty )\)
• C) increasing on \(( - \infty , 32 )\); decreasing on \(( 32 , \infty )\)
• D) increasing on \(( - \infty , 24 )\); decreasing on \(( 24 , \infty )\)
• E) increasing on \(( - \infty , 3 )\); decreasing on \(( 3 , \infty )\)

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Definitions:

ADH

Antidiuretic Hormone, a hormone that helps to control the balance of water in the body by affecting the kidneys.

Water Reabsorption

The process by which water is taken back into the body from the filtrate produced by the kidneys during urine formation, thus maintaining fluid balance.

Collecting Ducts

The structures in the kidneys that receive urine from the nephrons and transport it into the renal pelvis, playing a key role in water and ion balance.

Filtrate Osmolality

Filtrate osmolality refers to the concentration of solutes in the fluid that is filtered through the body's cells or organs, important in the regulation of water and solute balance.