Find the Function with the Given Derivative Whose Graph Passes $\mathrm { r } ^ { \prime } ( \theta ) = 4 + \sec ^ { 2 } \theta , \mathrm { P } \left( \frac { \pi } { 4 } , 0 \right)$

question 124

Multiple Choice

Find the function with the given derivative whose graph passes through the point P.
- $\mathrm { r } ^ { \prime } ( \theta ) = 4 + \sec ^ { 2 } \theta , \mathrm { P } \left( \frac { \pi } { 4 } , 0 \right)$

• A) \(r ( \theta ) = 4 \theta + \tan \theta - \pi - 1\)
• B) \(r ( \theta ) = 4 \theta + \frac { 1 } { 3 } \sec ^ { 3 } \theta\)
• C) \(r ^ { \prime } ( \theta ) = 2 \theta ^ { 2 } + \tan \theta + \pi\)
• D) \(r ( \theta ) = 2 \theta ^ { 2 } + \tan \theta - \pi - 1\)

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Definitions:

Temperature

A measure of the thermal energy of a system, indicating how hot or cold it is.

Gas Particles

The small, discrete units that compose gases, moving freely and randomly and often described by the kinetic molecular theory.

Distances

Measurements of the space between two points, which can be measured in various units such as meters, miles, or light-years, depending on the context.

Gas Particles

The smallest constituents of a gas, moving freely and randomly, and obeying the gas laws.