Find an Equation of the Tangent Plant to the Surface $z = e ^ { x + y }$

question 28

Multiple Choice

Find an equation of the tangent plant to the surface $z = e ^ { x + y }$ at the point $( 0,0,1 )$ .

• A) \(z = x + y + 1\)
• B) \(z = e x + e y - 2 e + 1\)
• C) \(z = 2 x + 2 y + 1\)
• D)\(z = 2 e x + 2 e y - 4 e + 1\)
• E) \(z = 4 x + 4 y - 7\)
• F) \(z = e ^ { 2 } x + e ^ { 2 } y - 2 e ^ { 2 } + 1\)
• G) \(z = 2 e ^ { 2 } x + 2 e ^ { 2 } y - 4 e ^ { 2 } + 1\)
• H) \(z = 4 e x + 4 e y - 8 e + 1\)

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Definitions:

Blood Glucose

The main type of sugar found in the blood and the body's main source of energy.

Ghrelin Production

The process by which the stomach produces the hormone ghrelin, which stimulates appetite and signals the body to eat.

Leptin Levels

A measure of the hormone leptin, which is produced by fat cells and is involved in regulating appetite and energy balance.

PYY

A hormone involved in appetite regulation, produced in the gut in response to eating.