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 instantaneous 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

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

The slope is equal to m

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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