Find the Second Derivative of the Function $f ( x ) = 3 + 8 x \ln x$

question 94

Multiple Choice

Find the second derivative of the function $f ( x ) = 3 + 8 x \ln x$ .

• A) \(f ^ { \prime \prime } ( x ) = 8 + \frac { 8 } { x }\)
• B) \(f ^ { \prime \prime } ( x ) = \frac { 8 } { x }\)
• C) \(f ^ { \prime \prime } ( x ) = 8\)
• D) \(f ^ { \prime \prime } ( x ) = \frac { 16 } { x }\)
• E) \(f ^ { \prime \prime } ( x ) = 8 + \frac { 16 } { x }\)

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Definitions:

Ordinary Simple Interest

Interest calculated on the principal amount only, without compounding, usually over a period of a year or less.

360-Day Year

A financial convention or calculation basis where the year is assumed to consist of 360 days rather than 365 or 366 days, often used in interest rate calculations.

Ordinary Simple Interest Rate

The standard method of calculating interest, typically based on the original loan amount, rate, and time.

360-Day Year

A conventional method in finance where the year is assumed to have 360 days for simplifying interest rate calculations, commonly used in commercial lending.