This discussion re-visits the concept of optimization studied in Module 5. 1. Formulate an application problem...

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This discussion re-visits the concept of optimization studied in Module 5. 1. Formulate an application problem that could be modeled mathematically through the graph of the function 2c from Discussion 1. [Note: That graph was to have one horizontal asymptote and no vertical asymptote; and, to ensure that the entire 2c function was in the positive half-plane.] Some examples are the cost functions (manufacturing, production, distribution, transportation, installation, setup, etc.), economy charts, population functions, and modeling an epidemic. For further assistance, newspapers, magazines, and news sites are filled with various data and corresponding graphs. 2. Answer the following questions: For what values of the independent variable does the function have a practical interpretation in the context of your application problem? Explain. o In Desmos, draw the graph of the first derivative function and interpret it in the context of your application problem. Find all values, for which the first derivative of the function is 0 and interpret them in the context of your application problem. [My Hint: Remember that the 1st. Der. gives the slope of a tangent line to a curve (or an instantaneous rate of change, inst. velocity)... that there might be a relative maximum/minimum point in a curve when the tangent line is horizontal, with slope of 0.] o In Desmos, draw the graph of the second derivative function and interpret it in the context of your application problem. Find all values, for which the second derivative of the function is 0 and interpret them in the context of your application problem. [My Hint: Remember that the 2nd. Der. gives the concavity (opening up or opening down) in a curve, and when it (the 2nd. Der.) is 0, then there might be an inflection point in a curve.] There are multiple due dates in this assignment. Remember to use the Canvas Equation Editor. Refer to the Tools for Mathematics page in the Course Specific Information module for technical guidance. 2c function is y=x^2/x+1 This discussion re-visits the concept of optimization studied in Module 5. 1. Formulate an application problem that could be modeled mathematically through the graph of the function 2c from Discussion 1. [Note: That graph was to have one horizontal asymptote and no vertical asymptote; and, to ensure that the entire 2c function was in the positive half-plane.] Some examples are the cost functions (manufacturing, production, distribution, transportation, installation, setup, etc.), economy charts, population functions, and modeling an epidemic. For further assistance, newspapers, magazines, and news sites are filled with various data and corresponding graphs. 2. Answer the following questions: For what values of the independent variable does the function have a practical interpretation in the context of your application problem? Explain. o In Desmos, draw the graph of the first derivative function and interpret it in the context of your application problem. Find all values, for which the first derivative of the function is 0 and interpret them in the context of your application problem. [My Hint: Remember that the 1st. Der. gives the slope of a tangent line to a curve (or an instantaneous rate of change, inst. velocity)... that there might be a relative maximum/minimum point in a curve when the tangent line is horizontal, with slope of 0.] o In Desmos, draw the graph of the second derivative function and interpret it in the context of your application problem. Find all values, for which the second derivative of the function is 0 and interpret them in the context of your application problem. [My Hint: Remember that the 2nd. Der. gives the concavity (opening up or opening down) in a curve, and when it (the 2nd. Der.) is 0, then there might be an inflection point in a curve.] There are multiple due dates in this assignment. Remember to use the Canvas Equation Editor. Refer to the Tools for Mathematics page in the Course Specific Information module for technical guidance. 2c function is y=x^2/x+1