# 3.1 - Finding the slope of a tangent line using the...

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Finding the slope of a tangent line using the four-step process Definition of the Slope of a Tangent Line and Definition of the Derivative, f’(x). Finding the derivative of a function by use of the definition Rules (Shortcuts) for finding Derivatives Real World applications 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. . 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 (3, 1/3) {by the long way} Write an equation of the tangent line Derivative Rules: Rule 1: The Derivative of a Constant If f(x) = c, Then f ’(x) = 0. (If a function is constant, its instantaneous rate of change is zero, i.e. – it doesn’t change.) Rule 2: The Power Rule If f(x) = x n for any real number n, Then f ’(x) = n x n -1 . Rule 3 The Derivative of a constant times a function Is the constant times the

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3.1 - Finding the slope of a tangent line using the...

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