Prove that the function f given by f (x) = x² – x + 1 is neither strictly increasing nor strictly decreasing on (– 1, 1).

Question

Prove that the function f given by f (x) = x² – x + 1 is neither strictly increasing nor strictly decreasing on (– 1, 1).

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Hailey 3 weeks 2021-10-04T15:13:41+00:00 1 Answer 0 views 0

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    2021-10-04T15:15:09+00:00

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    12th

    Maths

    Application of Derivatives

    Increasing and Decreasing Functions

    Show that the function x2 -…

    MATHS

    Show that the function x

    2

    −x+1 is neither increasing nor decreasing on (0,1).

    December 26, 2019avatar

    Samruta Amizz

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    ANSWER

    Given,

    the function f(x)=x

    2

    −x+1

    f(x)=x

    2

    −x+1

    f

    (x)=2x−1

    f

    (x)>0, ∀x∈(

    2

    1

    ,1) [∵f

    (x)>0⇒ strictly increasing]

    f

    (x)<0,∀x∈(0,

    2

    1

    ) [∵f

    (x)<0⇒ strictly decreasing]

    clearly,

    we can see that

    f(x) is strictly increasing in the interval (

    2

    1

    ,1)

    f(x) is strictly decreasing in the interval (0,

    2

    1

    )

    ∴f(x) is neither increasing nor decreasing on the whole interval (0,1)

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