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Absolute max and min on an interval of a function with modulus or greatest integer terms

This type of question, asked 5 times: 14 Jun 2022, 26 Jun 2022, 25 Jul 2022, 31 Jan 2023, 1 Feb 2023. All 5 questions below, oldest first.

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  1. Question 1

    14 Jun 2022

    72
    The sum of absolute maximum and absolute minimum values of the function f(x)=∣2x2+3x−2∣+sin⁡xcosxf(x) =\left| 2x^{2}+ 3x - 2 \right|+ \sin xcosx in the interval [0,1]\lbrack 0,1\rbrack is :

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  2. Question 2

    26 Jun 2022

    68
    The sum of the absolute minimum and the absolute maximum values of the function f(x)=∣3x−x2+2∣−xf(x) =\left| 3x-x^{2}+ 2 \right|-x in the interval [−1,2]\lbrack - 1,2\rbrack is :

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  3. Question 3

    25 Jul 2022

    174
    The sum of the maximum and minimum values of the function f(x)=∣5x−7∣+[x2+2x]f(x) = |5x - 7| +\left\lbrack x^{2}+ 2x \right\rbrack in the interval [54,2]\left\lbrack \frac{5}{4},2 \right\rbrack, where [t]\lbrack t\rbrack is the greatest integer ≤t\leq t is

  4. Question 4

    31 Jan 2023

    160
    The absolute minimum value, of the function f(x)=∣x2−x+1∣+[x2−x+1]f(x) =\left| x^{2}- x + 1 \right|+\left\lbrack x^{2}- x + 1 \right\rbrack, where [t]\lbrack t\rbrack denotes the greatest integer function, in the interval [−1,2]\lbrack - 1,2\rbrack, is:

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  5. Question 5

    1 Feb 2023

    160
    The sum of the absolute maximum and minimum values of the function f(x)=∣x2−5x+6∣−3x+2f(x) =\left| x^{2}- 5x + 6 \right|- 3x + 2 in the interval [−1,3]\lbrack - 1,3\rbrack is equal to:

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