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    Statistics - Derivatives

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    Problem 1
    Given y = f(x) = x2 + 2x +3
    a) Use the definitional formula given below to find the derivative of the function.

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

    Problem 2

    Given, y = f(x) = 2 x3 - 3x2 + 4x +5
    a) Use the Power function to find derivative of the function.
    b) Find the value of the derivative at x = 4.

    Problem 3
    The revenue and cost functions for producing and selling quantity x for a certain production facility are given below.
    R(x) = 16x - x2
    C(x) = 20 + 4x
    a) Determine the profit function P(x).
    b) Use Excel to graph the functions R(x), C(x) and P(x) for the interval 0≤ x ≤ 12. Copy and paste the graph below. Note: Use Scatter plot with smooth lines and markers.
    c) Compute the break-even quantities.
    d) Determine the average cost at the break-even quantities.
    e) Determine the marginal revenue R'(x).
    f) Determine the marginal cost C'(x)
    g) At what quantity is the profit maximized?

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    https://brainmass.com/statistics/statistical-figures/statistics-derivatives-264496

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