Calculate the Derivative of the Function $\frac { \mathrm { ds } } { \mathrm { dt } } \mid \mathrm { t } = 0$

question 90

Multiple Choice

Calculate the derivative of the function. Then find the value of the derivative as specified.
- $\frac { \mathrm { ds } } { \mathrm { dt } } \mid \mathrm { t } = 0$ if $\mathrm { s } = \mathrm { t } ^ { 2 } - \mathrm { t }$

• A) \(\frac { \mathrm { ds } } { \mathrm { dt } } = 2 \mathrm { t } + 1 ; \frac { \mathrm { ds } } { \mathrm { dt } } \mid \mathrm { t } = 0 = 1\)
• B) \(\frac { \mathrm { ds } } { \mathrm { dt } } = 2 - \mathrm { t } ; \frac { \mathrm { ds } } { \mathrm { dt } } \mid \mathrm { t } = 0 = 2\)
• C) \(\frac { \mathrm { ds } } { \mathrm { dt } } = 2 \mathrm { t } - 1 ; \left. \frac { \mathrm { ds } } { \mathrm { dt } } \right| _ { \mathrm { t } = 0 } = - 1\)
• D) \(\frac { \mathrm { ds } } { \mathrm { dt } } = \mathrm { t } - 1 ; \frac { \mathrm { ds } } { \mathrm { dt } } \mid \mathrm { t } = 0 = - 1\)

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Definitions:

Average Rate

The mean value of a set of rates, calculated by dividing the sum of all rates by the number of rates.

Capital Investment

Funds invested in a business by the owners or shareholders to purchase capital assets or to retain in the business as working capital.

Asset Life

The expected period during which an asset is considered useful in the operations of a business, influencing depreciation calculations.

Average Rate

A calculation used to determine the mean value of a set of rates over a specified period, often applied in finance to find the average interest rate.