Differential Calculus and Optimization Quiz
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Questions and Answers

What is the process of finding the maximum and minimum point of a function called?

  • Optimization (correct)
  • Multi variable unconstrained optimization
  • Normative economic decision analysis
  • Differential Calculus

    • In a price-output decision-making problem, the objective may be to determine the output level that maximizes:

  • Cost of production
  • Normative economic decision analysis
  • Profits (correct)
  • Net present value of investments

    • What is the goal in a production problem according to the given text?

  • Maximize profits
  • Maximize net present value of investments
  • Select projects for capital budgeting
  • Minimize cost of producing a desired level of output (correct)

    • What is involved in normative economic decision analysis according to the text?

    <p>Determining the action that best achieves a desired goal or objective (C)</p> Signup and view all the answers

    What does the Second-Derivative Test for Optimum determine?

    <p>Maximum and minimum points of a function (A)</p> Signup and view all the answers

    What is the first order condition for optimization?

    <p>Finding the critical points by setting the first order derivative to zero (D)</p> Signup and view all the answers

    What is the process of finding the combination of inputs (resources) that minimizes the cost of producing a desired level of output called?

    <p>Constrained Optimization (D)</p> Signup and view all the answers

    What is the first order derivative used for in optimization?

    <p>Finding the rate of change of a function (D)</p> Signup and view all the answers

    What makes the first order condition for optimization sufficient to indicate an optimal point?

    <p>First Derivative Test (C)</p> Signup and view all the answers

    When is a point considered to be a maximum according to the First Derivative Test?

    <p>If the first derivative changes from positive to negative (B)</p> Signup and view all the answers

    According to the Second-Derivative Test, when is a point considered to be a maximum?

    <p>If the second derivative is less than 0 (B)</p> Signup and view all the answers

    What can be done if the sign of the second order derivative is not known?

    <p>Resort to the first order derivative test (A)</p> Signup and view all the answers

    What does the first order condition for optimization help find?

    <p>Critical points / stationary points (B)</p> Signup and view all the answers

    "If f’(x) has the same sign on both the immediate left and immediate right of point x*, it is neither maximum nor a minimum." What does this statement imply?

    <p>&quot;V&quot; shaped curves have no maximum or minimum points (C)</p> Signup and view all the answers

    What is the condition used to find the critical points or stationary points in optimization?

    <p>First order condition (B)</p> Signup and view all the answers

    Which test is used to determine if a point is a maximum or minimum according to the first order derivative test?

    <p>First Derivative Test (C)</p> Signup and view all the answers

    What does the second order derivative test determine about a point?

    <p>Both of the above (C)</p> Signup and view all the answers

    When is a point considered to be neither a maximum nor a minimum according to the First Derivative Test?

    <p>When the first derivative has the same sign on both sides of the point (C)</p> Signup and view all the answers

    What should be done if the sign of the second order derivative is not known when testing for optimality?

    <p>Resort to the First Derivative Test (B)</p> Signup and view all the answers

    What does normative economic decision analysis involve?

    <p>Determining the action that best achieves a desired goal or objective (C)</p> Signup and view all the answers

    What is the main goal in a capital budgeting problem?

    <p>Selecting projects that maximize the net present value of the investments chosen (D)</p> Signup and view all the answers

    What is the process of finding the maximum and minimum point of a function called?

    <p>Optimization (B)</p> Signup and view all the answers

    In a production problem, what is the goal related to the combination of inputs?

    <p>Finding the combination of inputs that minimizes the cost of producing a desired level of output (B)</p> Signup and view all the answers

    What is involved in solving normative economic decision analysis problems?

    <p>Determining the action that best achieves a desired goal or objective (C)</p> Signup and view all the answers

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