Problem 1
We'll use the product rule to say
h(x) = f(x)*g(x)
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)
Then plug in x = 2 and use the table to fill in the rest
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)
h ' (2) = f ' (2)*g(2) + f(2)*g ' (2)
h ' (2) = 2*3 + 2*4
h ' (2) = 6 + 8
h ' (2) = 14
<h3>Answer: 14</h3>============================================================
Problem 2
Now we'll use the quotient rule
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Problem 3
Use the chain rule
We are given:
There seems to be nothing I can do to simplify this equation. However, I can factor out an since they both have at least an
. Here is what we get:
This is in the simplest form I can get into. I cannot do anything more to simplify this expression. This is your final answer.
a.
Sally has $28.00 in her bank account and starts saving $18.25 every week.
Let x represent the number of weeks from when he have $28.00 in her account.
and y represent the amount in her account at week x;
We can write the function of the case as;
where m is the amount she saves every week, and b the initial amount in her account.
So, the function will be;
b.
Her friend Suzy has $161.00 in her bank account and is withdrawing $15 every week.
Using the same rule as in a above;
The function will be;
c.
The graph of the two functions is shown below;
d.
The point where the two lines intersect is shown in the graph above.
The point is at;
Which is at week 4 and balance $101.
e.
The point at which they intersect is the point where they both have the same values.
It is the week when both Sally and Suzy have the same amount in there account.
So, at the fourth week (week 4) Sally and Suzy both have $101 in their account
