+128406 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
