Nam owns a used car lot. He checked the odometers of the cars and recorded how far they had driven. He
2 answers:
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Answer: The meaning of each term of the Madison’s and Tyler’s expressions is mentioned below.
Step-by-step explanation:
Since, when Madison starts with a population of 1,000 amoebas that triples in size every hour for a number of hours, h.
That is, after 1 hour total number of amoebas = 3×1000 =
After 2 hour, total number of amoebas = 3×3000=
After 3 hour, total number of amoebas = 3×9000=
similarly, after h hours, total number of amoebas,
f(h) =
where, 1000 is the initial population of amoeba 3 is the growth factor of population and f(h) is the population of amoeba after h hours.
Since, when Tyler starts with a population of 1 amoeba that increases 30% in size every hour for a number of hours.
That is, after 1 hour total number of amoebas =
After 2 hour, total number of amoebas =
After 3 hour, total number of amoebas =
Similarly, after h hours, total number of amoebas,
f(h) =
Where, 1 is the initial population of amoeba, 0.3 is the growth rate and 1.3 is the growth factor.
Solution:
There is no saddle point (DNE). However, there is local maximum at (1, 1/2) for the given function.
Explanation:
we have function of two variables f(x,y)= 9-2x+4y-x^2-4y^2
we will find the values by partial derivative with respect to x,y,xy
= -2 -2x
= 4 -8y
to find the saddle point we should first find the critical points so equate
-2 -2x=0 and 4 -8y=0
we get x= 1 and y =1/2 so, critical points are (1,1/2)
to find local maximum or minimum we have to find ,
and
formula is *
-
=0
= -2
= -8
=0
putting values in formula
(-2)*(-8) -0 =16 > 0, and < 0 and
<0
so, here we have local maximum
we have no saddle point for this function by using the same formula we used to find extrema.
