What are the maximum and minimum of the function f(x) = 0.9 I -(x – 5) I + 7 ? A. Maximum at (5,7) and minimum at (0,0) B. Minimum at (5,7)

Question

What are the maximum and minimum of the function f(x) = 0.9 I -(x – 5) I + 7 ? A. Maximum at (5,7) and minimum at (0,0) B. Minimum at (5,7) and no maximum C. Minimum at (0,0) and no maximum D. Maximum at (5,7) and no minimum

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Vân Khánh 5 years 2021-08-03T23:32:49+00:00 1 Answers 16 views 0

Answers ( )

  1. ngocdiep
    0
    2021-08-03T23:34:22+00:00
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    Answer:

    Minimum = (5,7)

    No maximum

    Step-by-step explanation:

    Given

    f(x) = 0.9|-(x - 5)| + 7

    Solving (a): The minimum

    The minimum is when the absolute parameter gives 0

    i.e.

    0.9|-(x - 5)| =0

    Divide both sides by 0.9

    |-(x - 5)| =0

    Open bracket

    |-x + 5| =0

    Remove absolute sign

    -x + 5 =0

    Collect like terms

    x = 5

    Then the y value is:

    f(x) = 0.9|-(x - 5)| + 7

    Recall that: 0.9|-(x - 5)| =0

    So, we have:

    f(x) = 0 + 7

    f(x) = 7

    Hence, the minimum is at: (5,7)

    Since the minimum is at (5,7), then the graph will open upwards.

    Hence. the function has no maximum; i.e.

    Maximum = (\infty,\infty)

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