Cost of Producing 101st Item | Solve C(x) Function

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The cost function for production of a commodity is given below.
C(x) = 369 + 21x - 0.08x^2 + 0.0006x^3

Find the actual cost of producing the 101st item. (Round the answer to the nearest cent.)

i know that
c'(x) = 21-.16x+.0018x^2

but for the life of me cannot figure out how to find the answer
 
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How is "actual cost" defined?
 
How much does it cost to produce 101 items?

How much does it cost to produce 100 items?

So what was the cost of that 101st item?

The derivative is irrelelvant here. This is purely and arithmetic problem.
 
ive tried to just input the number and it keeps telling me that its the wrong answer I've done it every way i know how aghh
 
ooo nevermind, i just got it...i feel dumb lol
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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