Derivatives and Tangent Lines 3

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?