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An absolute maximum or minimum must occu...

An absolute maximum or minimum must occur at a critical point or at an end point

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What is critical point?

Find the absolute maximum and minimum values of each of the following in the given intervals : f(x)=x^(3)" in "[-2, 2] .

Knowledge Check

  • At critical point :

    A
    latent heat becomes infinite
    B
    liquid state is not possible
    C
    gaseous state is not possible
    D
    none of the above

  • At critical point :

    A
    latent heat becomes infinite
    B
    liquid state is not possible
    C
    gaseous state is not possible
    D
    none of the above

  • Beyond the critical point of H _(2)O

    A
    `H_(2)O` exists in a state of equilibrium with all phases
    B
    liquid water can no longer exist
    C
    only the solid phase can exist
    D
    `H_(2)O` can no longer exist as a molecule

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    Find the absolute maximum and minimum values of each of the following in the given intervals : f(x)=sinx+cosx" in "[0, pi]

    The absolute maximum and minimum values of functions can be found by their monotonic and asymptotic behaviour provided they exist. We may agree that finite limits values may be reagarded as absolute maximum or minimum. For instance the absolute maximum value of (1)/(1+x^(2)) is unity. It is attained at x=0 while absolute maximum value of the same functions is zero which is a limiting value of (xrarrooorxrarr-oo) The absolute minimum and maximum values of the function (x^(2)-x+1)/(x^(2)+x+1) is

    The absolute maximum and minimum values of functions can be found by their monotonic and asymptotic behaviour provided they exist. We may agree that finite limits values may be reagarded as absolute maximum or minimum. For instance the absolute maximum value of (1)/(1+x^(2)) is unity. It is attained at x=0 while absolute maximum value of the same functions is zero which is a limiting value of (xrarrooorxrarr-oo) The absolute minimum value of the function (x-2)/(sqrt(x^(2)+1)) is

    The absolute maximum and minimum values of functions can be found by their monotonic and asymptotic behaviour provided they exist. We may agree that finite limits values may be reagarded as absolute maximum or minimum. For instance the absolute maximum value of (1)/(1+x^(2)) is unity. It is attained at x=0 while absolute maximum value of the same functions is zero which is a limiting value of (xrarrooorxrarr-oo) The function x^(4)-4x+1 will have.

    The maximum or minimum of the objective funtion occurs only at the corner points of the feasible region. This theorem is known as fundamental theorem of

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