Answer:
Step-by-step explanation:
Recall that the notion of the derivative of a function is the rate of change of it. So it kind of tells us how much the value of functioin changes as the independt variable increases or decreases. If it is positive, this means that the function will increase as the indepent variable increases, and if it is negative, that means that the function will decrease as the indepent variable increases.
a) Since f(x) is the number of units you can make out of x units of raw material, it is natural to think that the more material you have, the more units you can make, so we expect f'(x) to be positive.
b) The company buys each unit of raw material at the price w. So the product wx represents the total cost of the raw material used to produce f(x) units. Since each produced unit is sell at the price of p, then the product pf(x) represents the total income for selling all f(x) units.Recall that the profit is the difference between the total income and the total cost of production. Hence, the profit in this case is represented by the formula pf(x)-wx.
c) Recall that a function h(x) that is differentiable attains it's maximum when it's derivative is 0 and it's second derivative is negative.
In this case, we know that the derivative of the profit function, evaluated at x* must be 0, since it is a maximum. So, using the rules of derivation, we know that the derivative of the profit function is pf'(x)-w. Hence,
pf'(x*)-w =0. From where we know that f'(x*)=w/p.
9514 1404 393
Answer:
B, E
Step-by-step explanation:
Like terms are ones that have the same variable, or that have no variable at all.
There are two terms with y as the variable. These are like terms.
There are two constant terms (with no variable). These are like terms.
The like term pairs are ...
- 25y and -0.2y (B)
- -6 and -2 (E)
we have
we know that
so
the answer is in thousandths, because the denominator of the multiplication of the two fractions is one thousand
Plugging in the value "
" in the above expression, we have
<h3><u>Note</u>:-</h3>
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
