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.
A) 25% = 25/100 = 0.25
b) 18% = 18/100 = 0.18
c) 40% = 40/100 = 0.40
d) 2% = 2/100 = 0.02
e) 0.15% = 0.15/100 = 0.0015
The answer is = -3, hope this helps!
<em>My goodness, this is rather confusing in the way it is worded. Nevertheless, I will attempt to do what I can. Just please keep in mind that this is my own interpretation of the problem, and therefore could be... incorrect.</em>
<em>I think, to start out, we could set up the problem like so</em>
<em>15 + t ≥ 26</em>
<em>because t is not a set number. </em>
<em>Then all that is needed is to subtract 15 from both sides, and the equation becomes</em>
<em>t ≥ 11</em>
<em>So the resulting answer is t ≥ 11.</em>
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<em>I hope that my interpretation helps.</em>
<em>-Toremi</em>
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Mean (Average) 48
Median 47.5
Range 66
Mode 72, appeared 2 times
Geometric Mean 41.680398411848
Largest 81
Smallest 15
Sum 480
Count 10