Suppose f(x) is continuous on [2,8] and −4≤f′(x)≤5 for all x in (2,8). Use the Mean Value Theorem to estimate f(8)−f(2).

1 answer:

6 0

2≤x≤8 −4≤f′(x)≤5 f is continuous in differentable on [2,8] so we know there is c btw 2 and 8 such that f′(c)=f(8)−f(2)/8−2 And we know −4≤f′(c)≤5 => we have −4≤ f(8)−f(2)/8−2 ≤5

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I’m going to put $100,000 into an investment at the beginning of year 1. At the end of year 2, I am going to add $55,000 more to

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Answer:

19 years

Step-by-step explanation:

The attached spreadsheet shows the balance will be zero at the beginning of year 19, when the last $10,423.27 is withdrawn from the account.

One could argue that the "nearest year" is year 18, when the balance after the withdrawal is less than $10,000.

_____

In the attached spreadsheet, the ending balance is 1.082 times the beginning balance (after deposits and withdrawals), which is the ending balance of the year before (after deposits).

In year 1 the beginning balance has 100,000 added. In year 2, the ending balance has 55,000 added. In year 4 and every year after, the beginning balance as 20,000 subtracted.