# 2.6 - (3 1/3 Write the equation of the tangent line at this...

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2.6 Objectives Definition of the Slope of a Tangent Line Finding the slope of a tangent line using the four-step process Writing the equation of a tangent line Definition of the Derivative, f’(x). Finding the derivative of a function by use of the definition Real World application Slope of a Tangent LIne The slope of the tangent line to the graph of f at the point P (x, f(x)) is given by: lim f(x+h) – f(x) h → 0 h if it exists. Using the four-step process, find the slope f the tangent line to the graph of the function f(x) = 6x 2 at any point. 1. f(x+h) 2. f(x+h) – f(x) 3. f(x+h) – f(x) h 4. lim f(x+h) – f(x) h →0 h Using the four-step process, find the slope f the tangent line to the graph of the function f(x) = -7x 2 +9x -3 at any point. 1. f(x+h) 2. f(x+h) – f(x) 3. f(x+h) – f(x) h 4. lim f(x+h) – f(x) h →0 h Find the slope of the tangent line to f(x) = 1/x at the point

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Unformatted text preview: (3, 1/3). Write the equation of the tangent line at this point. Derivative of a function: • The derivative of a function f with respect to x is the function f ’ (read “f prime”) f ’(x) = lim f(x+h) – f(x) h → 0 h The domain of f ’ is the set of all x where the limit exists. Find the derivative of f(x) = -9x 2 + 6x -1 Real World Application: • During the construction of a high-rise building, a worker accidentally dropped his portable electric screwdriver from a height of 576 feet. After t seconds, the screwdriver had fallen a distance of s = 16t2 feet. • How long did it take the screwdriver to reach the ground? • What was the average velocity of the screwdriver between the time it was dropped and the time it hit the ground? • What was the instantaneous velocity of the screwdriver at the time it hit the ground?...
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## This note was uploaded on 10/07/2011 for the course MATH 1431 taught by Professor Vaughn during the Spring '08 term at LSU.

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2.6 - (3 1/3 Write the equation of the tangent line at this...

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