Given $f ( x ) = e ^ { x }$

question 107

Multiple Choice

Given $f ( x ) = e ^ { x }$ , $g ( x ) = 7 ^ { x }$ , and h(x) = g(x) f(x) , find $h ^ { \prime } ( x )$ .

• A) \(7 ^ { x } e ^ { x } ( \ln 7 - 1 )\)
• B) \(7 ^ { x } e ^ { x } ( \ln 7 + 1 )\)
• C) \(7 ^ { x } e ^ { x } ( \ln 7 )\)
• D) \(x 7 ^ { x - 1 } e ^ { x - 1 } ( \ln 7 )\)

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Definitions:

Returns to Scale

The rate at which output increases in response to proportional increases in all inputs.

Production Function

An equation or graph that shows the output generated from different combinations of inputs, usually focusing on labor and capital.

Marginal Product

The increase in output that results from an additional unit of input.

Returns to Scale

Refers to the rate at which output increases as inputs are proportionately increased, categorizing into increasing, constant, or decreasing returns.