Quiz on Derivatives and Rates of Change

What is the derivative of a constant function?

• It is undefined.

• It is one.

• It is zero.

• It is the constant itself.

Who independently developed calculus alongside Isaac Newton?

• Gottfried Leibniz

• Carl Friedrich Gauss

• Albert Einstein

• René Descartes

What does the derivative represent in terms of a function?

• The area under the curve.

• The slope of the tangent line.

• The maximum value of the function.

• The average value of the function.

If a function is differentiable at a point, what can be said about its continuity at that point?

• It is always decreasing.

• It is always increasing.

• It may be discontinuous.

• It must be continuous.

What is the average velocity of an object defined as?

• The instantaneous rate of change.

• The derivative of the position function.

• The total time divided by total distance.

• The total distance divided by total time.

Which of the following is a rule for finding derivatives?

• The Sum Rule

• Both A and C

• The Average Rule

• The Constant Rule

What is the instantaneous rate of change of a function at a point?

• The integral of the function.

• The second derivative.

• The average rate of change.

• The derivative at that point.

How do you calculate the derivative of a product of two functions?

• By multiplying their derivatives.

• Using the Product Rule.

• By adding their derivatives.

• Using the Quotient Rule.

What is the Chain Rule used for?

• To find the integral of a function.

• To find the derivative of a product.

• To find the derivative of a composite function.

• To find the average rate of change.

What does the term 'marginal cost' refer to?

• The total cost of production.

• The cost of producing one additional unit.

• The average cost of production.

• The fixed cost of production.