2. Apollonius was a Greek mathematician known as 'The Great Geometer'. His works had a very great influence on the development of mathematics and his famous book Conics introduced the terms parabola, ellipse and hyperbola. Apollonius of Perga 262 – 190 B.C. Apollonius of Perga 262 – 190 B.C.

6. y = f (x) a f (a) x y (a, f (a)) Tangent Line Secant Line x (x, f (x)) Secant vs Tangent Lines Definition 1 Difference Quotient Average Rate of Change Instantaneous Rate of Change Slope of Secant Line

7. 1

8. y = f (x) a f (a) x y (a, f (a)) Tangent Line Secant Line h a + h (a + h, f (a + h)) Secant vs Tangent Lines Definition 2 Difference Quotient Average Rate of Change Instantaneous Rate of Change Slope of Secant Line

9. 2

10. Find the equation of the tangent line at a = 3.

11. Secant vs Tangent Lines Definitions 3 and 4

14. Hence,

15. Find the equation of the tangent line at a = 4.

16. “The derivative of f with respect to x is …” There are many ways to write the derivative of There are other forms that represent the derivative of the function f.

17. “f prime x”or “the derivative of f with respect to x” “y prime” “dee why dee ecks” or “the derivative of y with respect to x” “dee eff dee ecks” or “the derivative of f with respect to x” “dee dee ecks uv eff uv ecks”or “the derivative of f of x”

18. dx does not mean d times x dy does not mean d times y

19. does not mean (except when it is convenient to think of it as division.) does not mean (except when it is convenient to think of it as division.)

20. (except when it is convenient to treat it that way.) does not mean times

23. a.) b.)