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Unformatted text preview: c Kendra Kilmer February 19, 2009 Section 3.5 - Basic Differentiation Properties
Notation: Given y = f (x), then all represent the derivative of f at x. Constant Function Rule: If f (x) = c where c is a constant then Power Rule: If f (x) = xn , where n is a real number, then Constant Multiple Property: If f (x) = k g(x), where k is any real number, then Sum and Difference Property: If h(x) = f (x) g(x) where f and g are both differentiable functions, then Example 1:Differentiate the following functions: a) f (x) = 3 b) f (x) = e c) f (x) = 5 8 d) f (x) = x4 7 c Kendra Kilmer February 19, 2009 e) f (x) = x1/2 f) f (x) = 3 x5 g) f (x) = 5 x2 h) y = 3x2 + 7x - 9 i) m(t) = 5t - t 1/2 + e j) k(x) = x3 + 4x2 - 17 + x x k) y = 3x2 + x4 5 x 8 c Kendra Kilmer February 19, 2009 Example 2: If a book is dropped from a building 400 feet tall, its height above the ground (in feet) after t seconds is given by s(t) = 400 - 16t 2 a) Compute s (t) and interpret. b) Compute s(2) and s (2) and interpret. c) When does the book hit the ground? d) What is the impact velocity? Example 3: If f (x) = 3x4 - 2x2 , where does the graph of the function have a horizontal tangent line? Section 3.5 Homework Problems: 1,5,9,11,23,31,35,39,43,47,51,55,61,63,71,75,83,89 and supplemental problems 9 ...
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