Maths-
General
Easy

Question

The interval of increase of the function f space left parenthesis x right parenthesis equals x minus e to the power of x plus t a n invisible function application open parentheses fraction numerator 2 pi over denominator 7 end fraction close parentheses is

  1. left parenthesis 0 comma infinity right parenthesis    
  2. left parenthesis negative infinity comma 0 right parenthesis    
  3. left parenthesis 1 comma infinity right parenthesis    
  4. left parenthesis negative 11 right parenthesis    

hintHint:

We are given a function. We have to find the interval for which it is increasing. We will take the first order derivative to find the answer

The correct answer is: left parenthesis negative infinity comma 0 right parenthesis


    The given function is f open parentheses x close parentheses equals x minus e to the power of x plus tan open parentheses fraction numerator 2 pi over denominator 7 end fraction close parentheses
    A function is said to be increasing when it’s first order derivative is positive.
    It means f’(x) > 0
    We will use this condition to find the answer.
    Taking the first order derivative of the given function.
    f(x) = x minus e to the power of x plus tan open parentheses fraction numerator 2 pi over denominator 7 end fraction close parentheses
    f’(x) = 1 – ex + 0

    Now for the function to be increasing,
    f'(x) > 0
    1 - ex > 0
    1 > ex
    e< 1
    Taking loge of both the sides. It means we are taking natural log on both the sides.
    xlogee < loge1
    x < 0           ...{ logee = 1 and loge1 = 0}
    x can have any value less than zero.
    There is no lower limit on x.
    So, the interval will be (-∞,0)

    For such questions, we should know different formulas of differentiation.

    Related Questions to study

    General
    physics-

    In experiment of the potentiometer wire A B of length 100 cm has a resistance of 10capital omega, It is connected in series with a resistance R and a cell of emf 2 volts and of negligible internal resistance. A Source of emf 10mV is balanced against a length of 40 cm of the potentiometer wire. What is the value of the external resistance?

    In experiment of the potentiometer wire A B of length 100 cm has a resistance of 10capital omega, It is connected in series with a resistance R and a cell of emf 2 volts and of negligible internal resistance. A Source of emf 10mV is balanced against a length of 40 cm of the potentiometer wire. What is the value of the external resistance?

    physics-General
    General
    Maths-

    The function f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x is

    For such questions, we should check the rules of increasing and decreasing function.

    The function f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x is

    Maths-General

    For such questions, we should check the rules of increasing and decreasing function.

    General
    maths-

    If the function fraction numerator c o s invisible function application x plus K s i n invisible function application x over denominator 2 c o s invisible function application x plus 3 s i n invisible function application x end fraction is decreasing in its domain then K E

    If the function fraction numerator c o s invisible function application x plus K s i n invisible function application x over denominator 2 c o s invisible function application x plus 3 s i n invisible function application x end fraction is decreasing in its domain then K E

    maths-General
    parallel
    General
    Maths-

    The function f space left parenthesis x right parenthesis equals 1 plus 1 over x is

    We have to see the rules for a increasing and decreasing function.

    The function f space left parenthesis x right parenthesis equals 1 plus 1 over x is

    Maths-General

    We have to see the rules for a increasing and decreasing function.

    General
    maths-

    If l to the power of 2 end exponent plus m to the power of 2 end exponent equals 1 then the maximum value of l plus m is

    If l to the power of 2 end exponent plus m to the power of 2 end exponent equals 1 then the maximum value of l plus m is

    maths-General
    General
    maths-

    The minimum value of the function f space left parenthesis x right parenthesis equals 3 t a n invisible function application x plus 4 c o t invisible function application x where x element of open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses is

    The minimum value of the function f space left parenthesis x right parenthesis equals 3 t a n invisible function application x plus 4 c o t invisible function application x where x element of open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses is

    maths-General
    parallel
    General
    physics-

    In the experiment of potentiometer wire A B is 100 cm long shown in figure When AC=40 cm, no deflection occurs in the galvanometer. What is the value of R ?

    In the experiment of potentiometer wire A B is 100 cm long shown in figure When AC=40 cm, no deflection occurs in the galvanometer. What is the value of R ?

    physics-General
    General
    physics-

    Consider the potentiometer circuit shown. The potentiometer wire is 600 cm long and having restance 15r At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer?

    Consider the potentiometer circuit shown. The potentiometer wire is 600 cm long and having restance 15r At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer?

    physics-General
    General
    physics-

    Circuit for the measurement of resistance by potentiometer is shown. The galvanometer is first connected at point-A and zero-deflection is observed at length PJ=10 cm. In the second case, it is connected at a point C and zero deflection is observed at a length 30 text end text c m from P. Then what is the unknown resistance X?

    Circuit for the measurement of resistance by potentiometer is shown. The galvanometer is first connected at point-A and zero-deflection is observed at length PJ=10 cm. In the second case, it is connected at a point C and zero deflection is observed at a length 30 text end text c m from P. Then what is the unknown resistance X?

    physics-General
    parallel
    General
    physics-

    The current taken from the 30 V supply and the current through the 6capital omega resistor are respectively.

    The current taken from the 30 V supply and the current through the 6capital omega resistor are respectively.

    physics-General
    General
    physics

    common base amplifier circuit, calculate the change in base current if that in the collector current is 2 mA and alpha=0.98

    common base amplifier circuit, calculate the change in base current if that in the collector current is 2 mA and alpha=0.98

    physicsGeneral
    General
    physics

    The current gain of a transistor in common base mode is 0.99. To change the emitter current by 5 mA. What will be the necessary change in collector current?

    The current gain of a transistor in common base mode is 0.99. To change the emitter current by 5 mA. What will be the necessary change in collector current?

    physicsGeneral
    parallel
    General
    physics

    In a transistor amplifier β=62,R subscript L=5000Ω  and internal resistance of the transistor is 500Ω. What will be the ratio of power amplification to voltage amplification?

    In a transistor amplifier β=62,R subscript L=5000Ω  and internal resistance of the transistor is 500Ω. What will be the ratio of power amplification to voltage amplification?

    physicsGeneral
    General
    physics

    In a transistor, a change of 8.0 in the emitter current produces a change of 7.8 mA in the collector current. What change in the base current is necessary to produce the same change in the collector current?

    In a transistor, a change of 8.0 in the emitter current produces a change of 7.8 mA in the collector current. What change in the base current is necessary to produce the same change in the collector current?

    physicsGeneral
    General
    physics

    A transistor is connected in common emitter configuration. The collector supply is 8V  and the woltage drop across a resistor of 800 in the collector circuit is  0.5V. If the current gain factor alpha  is 0.96, then base current will be.........

    A transistor is connected in common emitter configuration. The collector supply is 8V  and the woltage drop across a resistor of 800 in the collector circuit is  0.5V. If the current gain factor alpha  is 0.96, then base current will be.........

    physicsGeneral
    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.