Derivatives and Tangent Lines 4

In this lesson, we learn about the formula for the derivative and how it gives us the slope of a tangent line to a curve. We see how to find the derivative for a linear function and how the slope of the tangent line is the same as the slope of the line itself. We also practice finding the derivative for a quadratic function and seeing how the slope of the tangent line varies at different points on the curve.

An introduction to derivatives and tangent lines to curves.

• What is the formal definition of a derivative?
• What does the derivative of a function tell you?
• How can you find the slope of a tangent line to a curve at a point on a curve?
• How do you find the derivative of a line?
• If f(x) = 3x - 2, what is f'(x)?
• How can you find the derivative of f(x) = 3x - 2 using the formal definition of a derivative?
• What is the derivative of f(x) = mx + b?
• If f(x) = 2 - x^2, how do you find f'(x) using the formal limit definition of a derivative?
• What is the slope of the tangent line to f(x) = 2 - x^2 at (0, 2) and (2, -2)?