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

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

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