Derivatives and Tangent Lines 3

In this lesson, we learn about derivatives and tangent lines. We start by using the definition for the slope of the tangent line to find the slope of the tangent line of a parabolic function. Then we use the point-slope formula to find the equation of the tangent line. Moving on, we learn the formal definition of a derivative, which is the limit as h approaches 0 of the difference quotient. We apply this definition to find the derivative of the same parabolic function and discover that we can find the slope of the tangent line at any point on the curve of the function by plugging in the x-value of the ordered pair into the derivative.

An introduction to derivatives and tangent lines to curves.

• What is the slope of the tangent line of f(x) = x^2 - 3 at (1, -2)?
• How do you find the slope of a tangent line to a curve at a point using the formal definition of a derivative?
• If you know the slope of the tangent line to a curve at a point, how can you use the point-slope formula to find the equation of the tangent line?
• How can you find the equation of the tangent line to a curve at a point?
• What is the definition of a tangent line with slope m?
• What is the formal definition of a derivative of a function?
• What is f'(x) = lim (x -> 0) (f(x+h) - f(x))/h?
• If f(x) = x^2 - 3, how do you find f'(x) using the formal definition of a derivative?
• What is the limit as h goes to 0 of 2x + h?
• Why is the derivative of f(x) = x^2 - 3 just 2x?