Find the Critical Point(s) of the Function

question 85

Multiple Choice

Find the critical point(s) of the function. Then use the second derivative test to classify the nature of each point, if possible. Finally, determine the relative extrema of the function.

• A) (1, 5) and (2, 5); saddle point: f(1, 5) = - 47; relative minimum value: f(2, 5) = - 48
• B) (1, 5) and (2, 5); relative maximum value: f(1, 5) = - 48; relative minimum value: f(2, 5) = 47
• C) (1, 5); saddle point: f(1, 5) = - 47
• D) (2, 5); relative maximum value: f(2, 5) = 48
• E) there are no critical points

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Definitions:

Equation

A mathematical statement that asserts the equality of two expressions.

Unit Change

A term describing the effect of a one-unit increase in the independent variable on the dependent variable in the context of statistical models, particularly regression analysis.

Regression Assumptions

Conditions that must be met for the regression analysis results to be valid, including linearity, independence, homoscedasticity, and normality of residuals.

F Distribution

A probability distribution that arises in the testing of whether two population variances are equal and in the analysis of variance (ANOVA) for comparing means among more than two groups.