Chapter 11.2, Problem 4E

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

# In Exercises 1–4, for each cost function, find the marginal cost at the given production level x, and state the units of measurement. (All costs are in dollars.) [HINT: See Example 1.] C ( x ) = 20 , 000 + 50 x + 10 , 000 x ; x = 100

To determine

To calculate: The marginal cost of cost function C(x)=20000+50x+10000x dollars at the production level x=100 and state the units of measurements.

Explanation

Given Information:

The cost function is C(x)=20000+50x+10000x and the production level is x=100.

Formula used:

Sum and Difference rule of derivative, [fĀ±g]ā²(x)=fā²(x)Ā±gā²(x).

Constant multiple rule is fā²(cx)=cfā²(x) where c is constant.

Power rule for finding the derivative of function is, y=xn is dydx=nxnā1, where n is any constant.

Derivative of constant is 0.

Calculation:

Consider the function, C(x)=20000+50x+10000x

Convert the function to power form as,

C(x)=20000+50x+10000xā1

Apply sum and difference rule of derivative to the function C(x)=20000+50x+10000x with respect to x,

Cā²(x)=ddx(20000)+ddx(50x)+ddx(10000xā1)

Apply constant multiple rule

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