$\text { Use the Product Rule to differentiate } f ( u ) = \sqrt { u } \left( 5 - u ^ { 6 } \right) \text {. }$

question 117

Multiple Choice

$\text { Use the Product Rule to differentiate } f ( u ) = \sqrt { u } \left( 5 - u ^ { 6 } \right) \text {. }$

• A) \(f ^ { t } ( u ) = 6 u ^ { \frac { 11 } { 2 } } + \frac { 5 - u ^ { 7 } } { 2 \sqrt { u } }\)
• B) \(f ^ { t } ( u ) = - 6 u ^ { \frac { 13 } { 2 } } - \frac { 5 - u ^ { 6 } } { 2 \sqrt { u } }\)
• C) \(f ^ { t } ( u ) = 6 u ^ { \frac { 13 } { 2 } } - \frac { 5 - u ^ { 6 } } { 2 \sqrt { u } }\)
• D) \(f ^ { t } ( u ) = - 6 u ^ { \frac { 11 } { 2 } } + \frac { 5 - u ^ { 6 } } { 2 \sqrt { u } }\)
• E) \(f ^ { t } ( u ) = - 6 u ^ { \frac { 13 } { 2 } } + \frac { 5 - u ^ { 6 } } { 2 \sqrt { u } }\)

---

Definitions:

Higher Price Buyer

A buyer willing to pay more than the standard price, usually in exchange for premium service, faster delivery, or exclusive access to a product or service.

Expected Revenue

The amount of money a business anticipates receiving over a certain period, based on sales forecasts and pricing strategies.

Capacity Reserved

The portion of production capability or service capacity deliberately kept back or saved for a specific purpose or customer.

Spoilage

The deterioration or loss of goods, especially in perishable inventory, due to factors like time, temperature, or mishandling.