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

What is the approximation of the slope at point P?

<p>4.1 (C)</p> Signup and view all the answers

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

<p>5 (C)</p> Signup and view all the answers

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

<p>0 (A)</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<p>5 (A)</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 (D)</p> Signup and view all the answers

What does mpc stand for in economics?

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

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