Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

A function f is defined by f:x →x^3-x^2-8x+5 for x<a.its given that f is an increasing function. Find the largest possible value of a?

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  • 1 month ago

    f(x) = x³ - x² - 8x + 5

    f '(x) = 3x² - 2x - 8 = 0...at stationary points

    i.e. (3x + 4)(x - 2) = 0

    so, at x = -4/3 and x = 2

    Hence, we need to examine f '(x) for x < -4/3, -4/3 < x < 2 and for x > 2

    For, x < -4/3...i.e. x = -2 we have:

    f '(-2) = 3(-2)² - 2(-2) - 8 > 0

    for -4/3 < x < 2...i.e. x = 0 we have:

    f '(0) = 3(0)² - 2(0) - 8 < 0

    for x > 2...i.e. x = 3 we have:

    f '(3) = 3(3)² - 2(3) - 8 > 0

    so, f(x) is increasing for x < -4/3 and for x > 2

    Hence, if x < a...then a = -4/3

    See sketch below.

    :)> 

    Attachment image
  • Ian H
    Lv 7
    1 month ago

    f(x) = x^3 - x^2 - 8x + 5 See where f is increasing on this graph

    https://www.wolframalpha.com/input/?i=y+%3D+x%5E3+...

    Differentiate and set to zero to show turning points at x = -4/3 and x = 2

    Find the largest possible value of a where f is an increasing function for x<a.

    That should now be obvious to you.

  • Anonymous
    1 month ago

    Sorry, but your tewacher wants YOU  to find it. If you don't know how, get a proper tutor.

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