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A#25.5 Name:_________________________________________ Date:___________ Period:___ Normal Line Worksheet 1. Given f ( x) 2x 1 , answer the following questions. 2x 1 a) Use a graphing utility to graph f(x). b) Find the zeros of f(x). c) Calculate f ’(x). d) Determine those points where f(x) has a horizontal tangent. Justify your answers. e) Write the equation of the line tangent to the graph of f(x) at the point where x=1. f) A normal line is perpendicular to a tangent line at a given point. Write the equation of the normal line to the graph of f(x) at the point where x=1. a) Find the derivative of the following functions. 2. f(x) = (x3 + 1)(x2 – 2) 3. f ( x) 3 3x x2 4. f ( x) 1 2x 3x 1 5. f ( x) 5x 1 x 1 A#25.5