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Problem 1

Given y = f(x) = x2 + 2x +3

a) Use definitional formula given below to find out the derivative of the function.

1106_definitional formula.jpg

b) Find out the value of the derivative at x = 3.

Problem 2

Given, y = f(x) = 2x3 - 3x2 + 4x +5

a) Use Power function to find derivative of the function.

b) Find out the value of derivative at x = 4.

Problem 3

The revenue and cost functions for selling and producing quantity x for a certain production facility are given below.

R(x) = 16x – x2

C(x) = 20 + 4x

a) Determine profit function P(x).

b) Use Excel to graph the functions R(x), C(x) and P(x) for interval 0≤ x ≤ 12. Copy as well as paste the graph below. Note: Use Scatter plot with smooth markers and lines.

c) find out the break-even quantities.

d) Determine average cost at the break-even quantities.

e) Determine marginal revenue R’(x).

f) Determine marginal cost C’(x)

g) At what quantity is the profit maximized?

Statistics and Probability, Statistics

  • Category:- Statistics and Probability
  • Reference No.:- M91516

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