Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

Given a function find where decreasing ?

Given f(x)=3x-2/x+5

Use interval notation, find where f(x) in decreasing? 

For increasing I got negative infinity to negative five, union, negative five to positive infinity 

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  • 1 month ago

    f(x) = (3x - 2)/(x + 5)

    or, f(x) = 3(x + 5)/(x + 5) - 17/(x + 5)

    so, f(x) = 3 - 17/(x + 5)

    => f(x) = 3 - 17(x + 5)⁻¹

    Hence, f '(x) = 17/(x + 5)²

    x = -5 is excluded from the domain

    For values less than -5 or greater than 5, (x + 5)² is positive, so 17/(x + 5)² as positive.

    So, for all values of the domain except x = -5, the function is increasing, i.e. never decreasing

    A sketch is below.

    :)> 

    Attachment image
  • 1 month ago

    f'(x) = 3 + 2/x^2

    This is always positive so it is not decreasing anywhere.

  • 1 month ago

    It's increasing everywhere except where it's undefined (at -5 ) so I agree; means it never decreases

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