Refer to the graph of (x) = 2x in Figure 18. (a) Explain graphically why, for h
Question:
Refer to the graph of ƒ(x) = 2x in Figure 18.
(a) Explain graphically why, for h > 0,
(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)?
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a In the graph the inequality holds for positive values of h since the difference quotient is an inc...View the full answer
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