Chapter 3 Section 01

# Chapter 3 Section 01 - Chapter 3 Section 01 Definition of...

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1 Chapter 3 Section 01 Definition of the Derivative

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2 Objectives: 1. Find the slope of a secant line to a curve through two given points. 2. Find the slope of a tangent line to a curve through a given point. 3. Compute the derivative, f’(a), for a given value of “a.” 4. Find the equation of the line tangent to a curve at a given point. 5. Find the derivative of linear and constant functions. 6. Estimate the derivative from a table of values. 7. Given an expression for the derivative, find the original function.
3 1 2 3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 x y (2, 10) (1, 2) M = (10-2)/(2-1) = 8

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4 1 2 3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 x y (1.5, 4.875) (1, 2) M=(4.875, - 2) / (1.5 – 1) = 5.75
5 1 2 3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 x y (1.1, 2.431) (1, 2) M = (2.431 – 2) / (1.1 – 1) = 4.31

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6 1 2 3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 x y
7 Formulas:    a b f(a) f(b) m(secant) slope   has   f(b)) (b,   to   f(a)) (a,   from   line   secant   The - - = h f(a) - h) f(a a - h a f(a) - h) f(a m(secant) + = + + = If we let b = a + h, where h is the distance from a to b.

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Chapter 3 Section 01 - Chapter 3 Section 01 Definition of...

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