If $f ( x ) = 5 ^ { x }$

question 6

Essay

If $f ( x ) = 5 ^ { x }$ , show that $\frac { f ( x + h ) - f ( x ) } { h } = 5 ^ { x } \left( \frac { 5 ^ { h } - 1 } { h } \right)$ .

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Definitions:

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Cost-Benefit Analysis

A systematic approach to estimate the strengths and weaknesses of alternatives used to determine options that provide the best approach to achieve benefits while preserving savings.

Risk-Benefit Analysis

A process of comparing the potential risks and benefits associated with a decision or action, often used in the context of health and safety, business, and environmental policy.

Law of Negligence

A legal principle where a person is held responsible for failing to take reasonable care, resulting in damage or harm to another.