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MAT 120 Exam 3 Concepts with 100- correct answers.
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MAT 120 Exam 3 Concepts with 100- correct answers.
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MAT 120 Exam 3 Concepts with100% correct answers
If 𝑦 = 𝑓 ( 𝑥 ) = 𝑥 n, where n is a real number, then f ′ ( x ) =
n x n − 1 - answer Theorem Power Rule
If 𝑦 = 𝑓 ( 𝑥 ) = 𝑘 ⋅ 𝑢 ( 𝑥 ), where 𝑘 is a real number and 𝑢 ( 𝑥 )
is a function, then f ′ ( x ) = k ⋅ u ′ ( x ). - answer Theorem
Constant Multiple Property
Theorem: Constant Function Rule
If y = f ( x ) = C is the constant function, then the
derivative is - answer 0 or zero
If y = f ( x ), then f ′ ( x ), y ′, d y d x, and d d x f ( x )all
represent the _______________ of f at x. - answer Derivative
If y = f ( x ) = u ( x ) ± v ( x ), where u ( x ) and v ( x ) are
functions, then f ′ ( x ) = u ′ ( x ) ± v ′ ( x ). - answer
Theorem Sum and Difference property
Let x be the number of units of a product produced in
some time interval. If C ( x ) is the total cost, R ( x ) is the
total revenue, and P ( x ) is the total profit, then - answer
C ′ ( x ) is the marginal cost
R ′ ( x ) is the marginal revenue
P ′ ( x ) is the marginal profit
, marginal profit = - answer (marginal revenue - marginal
cost)
Suppose C ( x ), R ( x ), and P ( x ) are the total cost,
revenue, and profit of producing x items. Match the
descriptions to the functions. - answer exact additional
cost
C(x + 1) - C(x)
approximate additional cost
C'(x)
exact additional revenue
R(x + 1) - R(x)
approximate additional revenue
R'(x)
exact additional profit
P(x + 1) - P(x)
approximate additional profit
P'(x)
Suppose C ( x ), R ( x ), and P ( x ) are the total cost,
revenue, and profit of producing x items. Match the
descriptions to the functions.
1.C ¯ ( x ) = C ( x ) x
2.R ¯ ( x ) = R ( x ) x
3.P ¯ ( x ) = P ( x ) x
4.C ¯ ′ ( x )
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