Find a Formula for the Slope of the Graph Of f

question 221

Multiple Choice

Find a formula for the slope of the graph of $f$ at the point $( x , f ( x ) )$ .Then use it to find the slope at the given point. $f ( x ) = \frac { 1 } { x + 8 } , \quad \left( 0 , \frac { 1 } { 8 } \right)$

• A) \(\begin{array} { l }
• m = \frac { 1 } { ( x + 8 ) ^ { 2 } } \\
• \text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = - \frac { 1 } { 64 }
• \end{array}\)
• B) \(\begin{array} { l }
• m = - \frac { 1 } { ( x + 8 ) ^ { 2 } } \\
• \text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = \frac { 1 } { 64 }
• \end{array}\)
• C) \(\begin{array} { l }
• m = - \frac { 1 } { ( x + 8 ) ^ { 2 } } \\
• \text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = - \frac { 1 } { 8 }
• \end{array}\)
• D) \(\begin{array} { l }
• m = - \frac { 1 } { ( x + 8 ) ^ { 2 } } \\
• \text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = - \frac { 1 } { 64 }
• \end{array}\)
• E) \(\begin{array} { l }
• m = \frac { 1 } { ( x + 8 ) ^ { 2 } } \\
• \text { At } \left( 0 , \frac { 1 } { 8 } \right) , m = \frac { 1 } { 64 }
• \end{array}\)

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Definitions:

Falling Costs

A situation where the expenses associated with producing a good or service decrease, often leading to lower prices for consumers.

Economies of Scale

The cost advantage that arises with increased output of a product, where average costs start to fall as production scales up.

Marginal Returns

denotes the additional output obtained by adding one more unit of a specific input, while keeping other inputs constant.

Diseconomies of Scale

The scenario where costs start increasing as a company or project becomes too large, leading to inefficiency.