Definition of Derivative

 Definition

  f‘(x): “f prime of x”  y‘ : “y prime” (what is a weakness of this notation?)  dy/dx : “dy dx” or, “the derivative of y with respect to x”  d/dx f(x) : “d dx of f at x” or “the derivative of f at x” Notation for derivatives

  Remember that the graph of the derivative f’(x) (the limit of the difference quotient) shows you the slope of f(x) at all values of x. Therefore…..  As f(x) is increasing….  f‘(x) is positive  As f(x) is decreasing…..  f‘(x) is negative…..  When f(x) has a horizontal tangent line (min or max)  f‘(x) has a zero at that x-value. Activity Summary