How do you estimate the instantaneous rate of

gabolzm6d

gabolzm6d

Answered question

2022-04-16

How do you estimate the instantaneous rate of change at the point for x=5 for f(x)=ln(x)?

Answer & Explanation

strasnihwhge

strasnihwhge

Beginner2022-04-17Added 14 answers

Since f(x)=1x, the answer is just f(5)=15=0.2
When x=5 (so that y=f(5)=ln(5)1.609), small changes in x produce
changes in y that are about 5 times as small. For example, if x=0.1 (if x
changes from 5 to 5.1), then y=f(5.1)f(5)=ln(5.1)ln(5)0.0198,
which is about 5 times smaller than x=0.1

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