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**Unformatted text preview: **-Y1 = m (x - x ,)
the result from 8c) find a tangent line to the curve f(x) = -6Vx at x=4
X= 4 5 (4) = =6541=-6(2)=-12
4 - (- 12 ) = - 3 ( x - 4)
( 4, - 12 ) px-value
YATA = 3 ( x - 4
Ly-value
y- y, = m ( x-xi)
3 x + 2 4 + 12 = 0 +
+ 31.3 x 424 + 12 = 0
Zy = - 3x- 12
2
3 X = - 24- 12
2 - 3x ( x - 4 ) 3x+24 412=0 mixly =-3
2
Tangent Line - 3x+ 24+ 12= 0
2 X - 6
10. The cost in dollars of producing x tacos is given by C(x) =-0.00375x2 +1.5x +1000 for Os x s 180.
(a) Find the marginal cost function.
marginal
AC lim CCKth ) - c(x )
Cost
An
h-po
lim K[- 00375 h -. 0075 x+los]
C' (x ) =
. 0075 x + 1
*th ) - 00375 ( 2 th ) + 105 ( x th ) + 1000 - -.00375 ( x2 +6 2 + 2xth ) + "15/+ 105 h+ 10 --,00375 x2-, 0037542-. 06 375
*th ) = -, 00375h 2. 60395. zeh trash ( (xth) - ((x) =- 0037she-_0075 xh+ losh -h[-.0037shro075 x4105]
(b) Find and interpret the marginal cost at a production level of 100 tacos. Please use a complete sentence.
X = 160-B C'(x) DC'(100)
C' ( 100 ) = ( :00 75 # 100) + 1.5 - 6' (150) = -- 75 +1.5
9:75
The marginal cost of producing loo tacos is $10. 75.
(c) Find the exact cost to produce the 101" taco.
= 101-A C'(x) + C'Clot )
( 101) = ( :0075 . 101 ) + 1.5 - C'(Wi) = = 7575+1.5 - $0. 7425 - Estimate of
(101) = =,00 375 (101) + 1.9 (101) - C(100)
1112 . 5
$ $0. 74625 / DExact cost
11 13.25
Of lost talk
(d) Compare the answers to parts (b) and (c). How are they related?
The marginal cost is reduced as the number of
units that are produced increases, The cost of producing the tooth unit is
the cost of producing the 10Ist unit is $10. 74925. Therefore the me is reducing at unit
y - y, = m (x- x, )
4 - (- 12 ) = 3 ( x - 4)
5 of 5
YARD = 2 * + 6...

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- Fall '19