Advanced Mathematics

[Kipindi]

An actuary has determined that for a certain demographic group, the number of people surviving over the duration of a century can be modeled by f(x) = 400√ 100 − x, 0 ≤ x ≤ 100 where x represents the age of the person in years in the group and f(x) represents the number of people surviving. Evaluate and interpret f' (70).

 

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[Dr.Peterson]

An actuary has determined that for a certain demographic group, the number of people surviving over the duration of a century can be modeled by f(x) = 400√ 100 − x, 0 ≤ x ≤ 100 where x represents the age of the person in years in the group and f(x) represents the number of people surviving. Evaluate and interpret f' (70).

You probably mean f(x) = 400√(100 − x), not f(x) = 400√ 100 − x as you wrote it. I hope you see the difference.

Now try differentiating this. If you're having trouble doing that, rewrite it as a fractional power.