Find the Particular Solution That Satisfies the Differential Equation $f ^ { \prime } ( x ) = \frac { 1 } { 2 } x - 5$

question 33

Multiple Choice

Find the particular solution that satisfies the differential equation $f ^ { \prime } ( x ) = \frac { 1 } { 2 } x - 5$ and initial condition $f ( 4 ) = - 16$ .

• A) \(f ( x ) = \frac { 1 } { 5 } x ^ { 2 } - 5 x\)
• B) \(f ( x ) = \frac { 1 } { 7 } x ^ { 2 } + 5 x - 1260\)
• C) \(f ( x ) = \frac { 1 } { 4 } x ^ { 2 } - 5 x\)
• D) \(f ( x ) = \frac { 1 } { 4 } x ^ { 2 } - 5 x - 1260\)
• E) \(f ( x ) = \frac { 1 } { 5 } x ^ { 2 } + 5 x\)

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Definitions:

Factorial ANOVA

A statistical analysis method used to examine the effects of two or more categorical independent variables on a continuous dependent variable and their interactions.

Main Effects

The immediate effect an independent variable has on a dependent variable within an experimental setup.

Interaction Effects

Refer to how the relationship between two variables changes when a third variable is introduced.

Factorial ANOVA

A statistical test used to compare the means of more than two groups considering multiple independent variables.