Find an Equation of the Tangent Line at the Indicated $$w = g ( z ) = 4 + \sqrt { 6 - z } , ( z , w ) = ( 5,5 )$$

question 427

Multiple Choice

Find an equation of the tangent line at the indicated point on the graph of the function.
- $$w = g ( z ) = 4 + \sqrt { 6 - z } , ( z , w ) = ( 5,5 )$$

• A) \(w = - \frac { 1 } { 2 } z - \frac { 15 } { 2 }\)
• B) \(w = \frac { 1 } { 2 } z + \frac { 15 } { 2 }\)
• C) \(w = - \frac { 1 } { 2 } z + \frac { 15 } { 2 }\)
• D) \(w = \frac { 1 } { 2 } z - \frac { 15 } { 2 }\)

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Definitions:

Alkene

Unsaturated hydrocarbons with at least one double bond between carbon atoms, exhibiting properties like addition reactions.

(Z)-2-Chloro-4-Ethylhex-2-Ene

A geometric isomer of an organic compound characterized by a specific arrangement of atoms, including a chloride and ethyl group.

(Z)-1-Chloro-1-Fluoro-1-Butene

A geometric isomer of a chlorofluorinated butene, characterized by having the chlorine and fluorine on the same side of the double bond.

Carbon-Carbon Double Bond

A chemical bond between two carbon atoms involving four bonding electrons instead of the usual two, giving the molecule added stability and reactivity.