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Jan 30, 2018
edited by Guest  Feb 1, 2018
edited by Guest  Feb 1, 2018

#1
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4)If f(x)=2x^3 −5x^2 −7,find f(h−1).

So we have

2 (h - 1)^3  - 5(h - 1)^2  -  7   =

2( h^3  -  3h^2 +  3h - 1 )  -  5 (h^2 - 2h  + 1)  - 7   =

2h^3  - 6h^2  + 6h  -  2  -  5h^2  + 10h  -  5  -  7   =

2h^3  -  11h^2  +  16h  - 14

5)  Find the average rate of change of f (x) = 2x^2 − 5x −12 over the interval [–2,–2+h], whereh>0.

We have

[   (  2 ( -2 + h)^2  - 5 ( -2 + h) -  12)   -  ( 2(-2)^2 - 5(-2) - 12 )  ]  /  [ (- 2 + h)  - (-2) ]  =

[  (  2 (h^2 - 4h + 4)  + 10 - 5h - 12 )  -  ( 8  + 10 - 12 ) ]  /  h  =

[ 2h^2  -  8h  + 8  +  10  - 5h  - 12   - 8  - 10  + 12 ]  / h  =

[  2h^2   - 13h ] /  h   =

h ( 2h - 13)  /  h  =

2h - 13

6) The value of a boat is \$800,000 in year 2006 and it depreciates \$30,000 per year, after year 2006. Find a model to represent the boat’s value V(in \$1000) as a function of t. Variable t represents the number of years t after year 2006.

We have that

V(t)   =  800  -  30t

Where  V(t)  is the value in thousands, t years  after 2006   Jan 30, 2018