The Function $R ( t ) = 1,120 + 79 t - t ^ { 3 }$

question 7

Multiple Choice

The function $R ( t ) = 1,120 + 79 t - t ^ { 3 }$ represents the value of the U.S. dollar in Indian rupees as a function of the time t in days. Find the average rates of change of $R ( t )$ over the time intervals $[ t , t + h ]$ , where t is as indicated and $h = 1$ , $0.1$ , $0.01$ , and $0.0001$ days. Hence, estimate (using $h = 0.0001$ ) the instantaneous rate of change of $\text { R }$ at time $t = 2$ .
Select your answer rounded to the nearest whole number.

• A)63
• B) 69
• C) 64
• D) 67
• E) 68

---

Definitions:

Nonsystematic Standard Deviation

A measure of the variability of an investment's return due to factors specific to the investment or its issuer, excluding broader market influences.

Macroeconomic Risks

Considered broad economic or political uncertainties that could affect the performance of financial markets and investments globally.

Security Selection

The process of choosing individual securities for investment with the goal of achieving the best possible return for a given level of risk.

Passive Strategy

A portfolio decision that avoids any direct or indirect security analysis. See passive management.