Chapter 3 | Derivatives
321
Figure 3.33 The graph of E ( x ) = e x is between y =2 x and y =3 x .
For a better estimate of e , we may construct a table of estimates of B ′(0) for functions of the form B ( x ) = b x . Before doing this, recall that B ′(0) = lim x →0 b x − b 0 x −0 = lim x →0 b x −1 x ≈ b x −1 x for values of x very close to zero. For our estimates, we choose x =0.00001 and x =−0.00001 to obtain the estimate b −0.00001 −1 −0.00001 < B ′(0) < b 0.00001 −1 0.00001 .
See the following table.
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