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Unformatted text preview: of f at 0, that is, So f’ ( x ) = f’ (0) a x 1 '( ) lim h x h a f x a h →= 1 lim '(0) h h a f h →= EXPONENTIAL FUNCTIONS If f ( x ) = e x x, find f’ and f’’ . Compare the graphs of f and f’ . EXPONENTIAL FUNCTIONS Example 8 (3.1) The function f and its derivative f’ are graphed here. s Notice that f has a horizontal tangent when x = 0. s This corresponds to the fact that f’ (0) = 0 . EXPONENTIAL FUNCTIONS Example 8 Notice also that, for x > , f’ ( x ) is positive and f is increasing. When x < , f’ ( x ) is negative and f is decreasing. At what point on the curve y = e x is the tangent line parallel to the line y = 2 x ? EXPONENTIAL FUNCTIONS Example 9 (3.1) Thus, the required point is: ( a , e a ) = ( l n 2, 2) EXPONENTIAL FUNCTIONS Example 9...
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 Fall '08
 Noohi
 Calculus, Derivative, Exponential Functions, lim, 2 seconds

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