Refer to the graph of (x) = 2x in Figure 18. (a) Explain graphically why, for h

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Refer to the graph of ƒ(x) = 2x in Figure 18.
(a) Explain graphically why, for h > 0,

f(-h)-f(0) -h  f'(0)  f(h) - f(0) h

(b) Use (a) to show that 0.69314 ≤ ƒ'(0) ≤ 0.69315.
(c) Similarly, compute ƒ'(x) to four decimal places for x = 1, 2, 3, 4.
(d) Now compute the ratios ƒ'(x)/ƒ'(0) for x = 1, 2, 3, 4. Can you guess an approximate formula for ƒ'(x)?

1 + 2 -1 3 FIGURE 18 Graph of f(x) = 2*. X

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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