Unit 6: Understanding Derivatives and Marginal Product of Labor
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Questions and Answers

What does the slope of a curve at a particular point represent?

  • The total output of the function
  • The marginal product of labor
  • The instantaneous rate of change of the function (correct)
  • The average rate of change of the function

    • In the context of the given production function, what does the slope of the graph represent?

  • The marginal product of labor (correct)
  • The change in output for a fixed number of workers
  • The average product of labor
  • The change in number of workers for a fixed output

    • For a linear function y(x) = mx + c, what is the relationship between the function and its slope?

  • The slope is equal to m (correct)
  • The slope is equal to mx + c
  • The slope is equal to x
  • The slope is equal to c

    • What does the slope of a tangent to a curve at a particular point represent?

    <p>The instantaneous rate of change of the function</p> Signup and view all the answers

    Why do we need to know the slope of a function in many economic applications?

    <p>To determine the instantaneous rate of change of the function</p> Signup and view all the answers

    What is the approximation of the slope at point P?

    <p>4.1</p> Signup and view all the answers

    What is the slope at the point where x = 3?

    <p>5</p> Signup and view all the answers

    What is the derivative of a constant function f(x) = A?

    <p>0</p> Signup and view all the answers

    What is the derivative of a linear function f(x) = a + bx?

    <p>b</p> Signup and view all the answers

    What is the derivative of the function f(x) = x^n?

    <p>n * x^(n-1)</p> Signup and view all the answers

    What is the derivative of the natural exponential function f(x) = e^x?

    <p>e^x</p> Signup and view all the answers

    What is the derivative of the natural logarithmic function f(x) = ln(x)?

    <p>-1/x</p> Signup and view all the answers

    What is the derivative of the function f(x) = x^17?

    <p>-17 * x^16</p> Signup and view all the answers

    What is the derivative of the function f(x) = x^(-4)?

    <p>-4 * x^(-3)</p> Signup and view all the answers

    What is the derivative of the function f(x) = sqrt(x)?

    <p>(1/2) * x^(-1/2)</p> Signup and view all the answers

    What is the quantity demanded when p = 0 using q. 𝐶 =5+ 𝑝 ?

    <p>5</p> Signup and view all the answers

    What does the derivative dC/dp measure in the context where C is consumption and Y is income?

    <p>Change in quantity demanded with respect to price</p> Signup and view all the answers

    What does mpc stand for in economics?

    <p>Marginal propensity to consume</p> Signup and view all the answers

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