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.
Answer:
.797
Step-by-step explanation:
If your talking about a decimal number, you would say the <u>thousandth</u>. I know, weird, but don't blame me.
To round up, any number above 5 rounds up to the next value place, and any number below 5 rounds down to the last value place.
Ex: 1.3483838383
Since 8 is greater than 5, we could get rid of all the 83s and just round up to 1.35.
So the thousandths place in a decimal would be 0.79<u>6</u>66357977, so we just ask if the next number after the thousandths place is greater than 5. The place number after .796 is 6, so since it is greater than 5, we would round up to .797.
Our answer is .797.
Hope this helps!
Answer:
-2.5
Step-by-step explanation:
-30 + (-15) + (-20) + 55 = -10. Then you divide it by how many numbers there are (4). Which equals - 2.5. If this is wrong, then round up to -3.
Answer: 4x = -8
Reasoning:
Multiply both sides by 4
Answer:j
Step-by-step explanation:
