Math  /  Calculus

QuestionThe total cost (in dollars) of producing xx coffee machines is C(x)=1700+50x0.7x2C(x)=1700+50 x-0.7 x^{2} (A) Find the exact cost of producing the 21st machine.
Exact cost of 21st machine == \square (B) Use marginal cost to approximate the cost of producing the 21st machine.
Approx. cost of 21 st machine == \square

Studdy Solution
Use the marginal cost to approximate the cost of producing the 21st machine by evaluating C(x) C'(x) at x=20 x = 20 :
C(20)=501.4×20 C'(20) = 50 - 1.4 \times 20 C(20)=5028 C'(20) = 50 - 28 C(20)=22 C'(20) = 22
Approx. cost of 21st machine =22 = \boxed{22}

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