Finding Derivatives Using Limits

What is the purpose of computing the difference quotient when finding a derivative?

• To calculate the area under a curve

• To solve a differential equation

• To determine the slope of the tangent line

• To find the integral of a function

What is the function used in the example to find the derivative?

• 6x^5

• 5x^3

• 4x^4

• 3x^2

In the difference quotient, what do you replace x with?

• x - y

• x - h

• x + h

• x + y

What is the expanded form of (x + h)^3?

• x^3 + 2x^2h + h^3

• x^3 + 3x^2h + 3xh^2 + h^3

• x^3 + x^2h + h^3

• x^3 + 3xh + h^3

What happens to the terms 5x^3 and -5x^3 in the difference quotient?

• They cancel each other out

• They are multiplied

• They are divided

• They are added together

What is factored out from the numerator in the difference quotient?

• 5

• x^2

• h

• x

What is the limit of 15xh as h approaches zero?

• 0

• 15xh

• 15x

• 15x^2

What is the final derivative of the function 5x^3?

• 20x^2

• 10x^2

• 15x^2

• 25x^2

What is the purpose of taking the limit as h approaches zero?

• To find the maximum value

• To find the exact slope of the tangent line

• To find the average rate of change

• To find the minimum value

What will be learned in future lessons to avoid using limits for derivatives?

• Graphing methods

• Shortcut rules for derivatives

• Algebraic simplifications

• Integration techniques