ࡱ> `  bjbj 4 %       & & & 8^ , |  " !!!!!!2h! !   36X      & L0|RRR \!!kX|$B B        Math 151 Handout Examples: Using the Definition of the Derivative, Example 1: Use the definition of the derivative to find  EMBED Equation.3  if  EMBED Equation.3 . Solution: Using the limit definition of the derivative, we see that  EMBED Equation.3  Example 2: Find the equation of the line tangent to the graph of  EMBED Equation.3  at the point (0, -1). Solution: To find the equation of any line, including a tangent line, we need to know the lines slope and a point on the line. Since we already have a point on line, we must find the tangent lines slope, which is found using the derivative. Using the limit definition of the derivative, we see that  EMBED Equation.3  Continued on next page Using  EMBED Equation.3 , we can now find the slope at the give point (0, -1).  EMBED Equation.3 . Using  EMBED Equation.3 , we see that from the slope intercept equation  EMBED Equation.3  that  EMBED Equation.3  To find b, use the fact that at the point (0, -1),  EMBED Equation.3  and  EMBED Equation.3 . Thus  EMBED Equation.3  giving  EMBED Equation.3 . Thus, the equation of the tangent line is:  EMBED Equation.3 .      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