Find the Function with the Given Derivative Whose Graph Passes $f ^ { \prime } ( x ) = e ^ { 3 x } , P \left( 0 , \frac { 7 } { 3 } \right)$

question 112

Multiple Choice

Find the function with the given derivative whose graph passes through the point P.
- $f ^ { \prime } ( x ) = e ^ { 3 x } , P \left( 0 , \frac { 7 } { 3 } \right)$

• A) \(f ( x ) = e ^ { 3 x } + \frac { 7 } { 3 }\)
• B) \(f ( x ) = \frac { 1 } { 3 } e ^ { 3 x + 2 }\)
• C) \(f ( x ) = \frac { 1 } { 3 } e ^ { 3 x } + \frac { 7 } { 3 }\)
• D) \(f ( x ) = 3 e ^ { 3 x } + 2\)

---

Definitions:

Alcohol Congeners

Chemical compounds that occur naturally in alcoholic beverages alongside ethanol, contributing to their taste, aroma, and physiological effects.

1-butanol

An organic compound, also known as butyl alcohol, a four-carbon straight-chain alcohol with the chemical formula C4H9OH, used as a solvent and in the manufacture of other chemicals.

Structural Formula

A graphical representation showing the arrangement of atoms within a molecule, indicating how they are connected.

2-butanol

An organic compound, also known as sec-butanol, which is a type of alcohol with four carbon atoms and a secondary hydroxyl group.