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This is the problem I was trying to solve:

"Let $f(t)$ be the number of words a certain person learns per day when she is $t$ years old. What is the meaning of $f'(20)$? What are the units of measurement?"

I was thinking, since $f'(t)$ represents the slope on the graph, it means how fast a person can learn certain number of words per day at the age of $20$. But I'm also kinda confused. Could someone please help clarify this?? And also what would be the units of measurement?

M47145
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  • The derivative of a function at $t$ , $f'(t)$ is the rate of change of the function at that point.

    That means in this case that it represents how many words per year is the person learning at its 20th birthday

     – Bunder Mar 16 '13 at 22:14
  • @Bunder but f(t) already means how many words per day the person is learning at the age of t. I don't understand how you got "how many words per years the person learning at 20". could you clarify please? –  Mar 16 '13 at 22:25

2 Answers2

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f'(20) would correspond to the change of how many words a person learns per day at age 20.

The units of measurement is referring to the fact that in the case of the derivative there is a (# of words change)/(day).

It may help to think of an analogy of plotting a distance/time graph where x is some measure of time and f(x) represents some distance. f'(x) would be measured in distance/time is the point here.

JB King
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f'(20) is the acceleration of learning words per day at age 20. Is the difference between the learning speed (words per day) at 20 and the learning speed at 19 (this is very approximate because it is not a continuous function). The units of f is words/day, the units of f' would be words/(day year) (change of words per day, per year)

Wolphram jonny
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