Maths-
General
Easy

Question

The function f open parentheses x close parentheses equals x to the power of 3 end exponent plus a x to the power of 2 end exponent plus b x plus c comma a to the power of 2 end exponent less or equal than 3 b blank h a s

  1. One maximum value  
  2. One minimum value  
  3. No extreme value  
  4. One maximum and one minimum value  

The correct answer is: No extreme value


    Given, f open parentheses x close parentheses equals x to the power of 3 end exponent plus a x to the power of 2 end exponent plus b x plus c comma a to the power of 2 end exponent less or equal than 3 b
    On differentiating w.r.t. x comma we get

    f to the power of ´ end exponent open parentheses x close parentheses equals 3 x to the power of 2 end exponent plus 2 a x plus b

    Put f to the power of ´ end exponent open parentheses x close parentheses equals 0

    rightwards double arrow blank 3 x to the power of 2 end exponent plus 2 a x plus b equals 0

    rightwards double arrow blank x equals fraction numerator negative 2 a plus-or-minus blank square root of 4 a to the power of 2 end exponent minus 12 b end root over denominator 2 cross times 3 end fraction

    equals fraction numerator negative 2 a plus-or-minus 2 square root of a to the power of 2 end exponent minus 3 b end root over denominator 6 end fraction

    Since a to the power of 2 end exponent less or equal than 3 b,

    therefore blank x Has an imaginary value.

    Hence, no extreme value of x blankexist.

    Related Questions to study

    General
    Maths-

    How many real solutions does the equation x to the power of 7 end exponent plus 14 x to the power of 5 end exponent plus 16 x to the power of 3 end exponent plus 30 x minus 560 equals 0 have?

    How many real solutions does the equation x to the power of 7 end exponent plus 14 x to the power of 5 end exponent plus 16 x to the power of 3 end exponent plus 30 x minus 560 equals 0 have?

    Maths-General
    General
    Maths-

    If y equals x to the power of n end exponent comma then the ratio of relative errors in y and x is

    If y equals x to the power of n end exponent comma then the ratio of relative errors in y and x is

    Maths-General
    General
    Maths-

    If a and b are positive numbers such that a greater than b comma then the minimum value of a   sec invisible function application blank theta minus b tan invisible function application theta open parentheses 0 less than theta less than fraction numerator pi over denominator 2 end fraction close parentheses is

    If a and b are positive numbers such that a greater than b comma then the minimum value of a   sec invisible function application blank theta minus b tan invisible function application theta open parentheses 0 less than theta less than fraction numerator pi over denominator 2 end fraction close parentheses is

    Maths-General
    parallel
    General
    Maths-

    The side of an equilateral triangle is ´ a ´ units and is increasing at the rate of lambda blank u n i t s divided by s e c. The rate of increase of its area is

    The side of an equilateral triangle is ´ a ´ units and is increasing at the rate of lambda blank u n i t s divided by s e c. The rate of increase of its area is

    Maths-General
    General
    Maths-

    In how many ways four men and three women may sit around a round table if all the women are together.

    In how many ways four men and three women may sit around a round table if all the women are together.

    Maths-General
    General
    Maths-

    In how many ways 5 persons can sit at a round table, if two of the persons does not sit together.

    In how many ways 5 persons can sit at a round table, if two of the persons does not sit together.

    Maths-General
    parallel
    General
    Maths-

    The function f open parentheses x close parentheses equals fraction numerator x over denominator 2 end fraction plus fraction numerator 2 over denominator x end fraction has local minimum at

    The function f open parentheses x close parentheses equals fraction numerator x over denominator 2 end fraction plus fraction numerator 2 over denominator x end fraction has local minimum at

    Maths-General
    General
    Maths-

    On which of the following intervals is the function f open parentheses x close parentheses equals 2 blank x to the power of 2 end exponent minus log invisible function application open vertical bar x close vertical bar comma x not equal to 0 increasing?

    On which of the following intervals is the function f open parentheses x close parentheses equals 2 blank x to the power of 2 end exponent minus log invisible function application open vertical bar x close vertical bar comma x not equal to 0 increasing?

    Maths-General
    General
    Physics-

    A conducting circular loop is placed in a uniform magnetic field 0.04 blank T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 blank m m divided by s. The induced e m f in the loop when the radius is 2 blank c m is

    A conducting circular loop is placed in a uniform magnetic field 0.04 blank T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 blank m m divided by s. The induced e m f in the loop when the radius is 2 blank c m is

    Physics-General
    parallel
    General
    Physics-

    198.The transformation ratio in the step-up transformer is

    198.The transformation ratio in the step-up transformer is

    Physics-General
    General
    Physics-

    Two coils A and B having turns 300 and 600 respectively are placed near each other, on passing a current of 3.0 blank a m p e r e in A, the flux linked with A is 1.2 cross times 10 to the power of negative 4 end exponent blank w e b e r and with B it is 9.0 cross times 10 to the power of negative 5 end exponent w e b e r. The mutual inductance of the system is

    Two coils A and B having turns 300 and 600 respectively are placed near each other, on passing a current of 3.0 blank a m p e r e in A, the flux linked with A is 1.2 cross times 10 to the power of negative 4 end exponent blank w e b e r and with B it is 9.0 cross times 10 to the power of negative 5 end exponent w e b e r. The mutual inductance of the system is

    Physics-General
    General
    Physics-

    The magnetic flux across a loop of resistance 10 capital omega is given by ϕ equals 5 t to the power of 2 end exponent minus 4 t plus 1 blank w e b e r. How much current is induced in the loop after 0.2 sec

    The magnetic flux across a loop of resistance 10 capital omega is given by ϕ equals 5 t to the power of 2 end exponent minus 4 t plus 1 blank w e b e r. How much current is induced in the loop after 0.2 sec

    Physics-General
    parallel
    General
    Physics-

    A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A magnetic induction B constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere with part of the loop outside the field, as shown in figure. The induced emf is

    A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A magnetic induction B constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere with part of the loop outside the field, as shown in figure. The induced emf is
    Physics-General

    General
    Physics-

    At a place the value of horizontal component of the earth’s magnetic field His 3 cross times 10 to the power of negative 5 end exponent w e b e r divided by m to the power of 2 end exponent. A metallic rod A B of length 2 blank m placed in east-west direction, having the end A towards east, falls vertically downward with a constant velocity of 50 blank m divided by s. Which end of the rod becomes positively charged and what is the value of induced potential difference between the two ends

    At a place the value of horizontal component of the earth’s magnetic field His 3 cross times 10 to the power of negative 5 end exponent w e b e r divided by m to the power of 2 end exponent. A metallic rod A B of length 2 blank m placed in east-west direction, having the end A towards east, falls vertically downward with a constant velocity of 50 blank m divided by s. Which end of the rod becomes positively charged and what is the value of induced potential difference between the two ends

    Physics-General
    General
    Physics-

    A rectangular, a square, a circular and an elliptical loop, all in the left parenthesis x minus y right parenthesis plane, are moving out of a uniform magnetic field with a constant velocity stack V with rightwards arrow on top equals v blank stack i with rightwards arrow on top. The magnetic field is directed along the negative z-axis direction. The induced e m f, during the passage of these loops, out of the field region, will not remain constant for

    A rectangular, a square, a circular and an elliptical loop, all in the left parenthesis x minus y right parenthesis plane, are moving out of a uniform magnetic field with a constant velocity stack V with rightwards arrow on top equals v blank stack i with rightwards arrow on top. The magnetic field is directed along the negative z-axis direction. The induced e m f, during the passage of these loops, out of the field region, will not remain constant for

    Physics-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.