Question
is decreasing in

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Hint:
We are given a function. We have to find the interval for which it is decreasing. We will take the first order derivative to find the answer
The correct answer is:
The given function is f(x) = tan^{1}x  x
A function is said to be decreasing when it’s first order derivative is negative
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) = tan^{1}x  x
The negative sign make sures that the function is negative i.e. decreasing.
x can take any value of real number.
And the set of real numbers extends from ∞ to ∞.
So, the interval for which given function is decreasing is (∞, ∞)
We should know the formulas of differentiation. And, we should know the condition for increasing and decreasing function.
Related Questions to study
The interval of increase of the function is
For such questions, we should know different formulas of differentiation.
The interval of increase of the function is
For such questions, we should know different formulas of differentiation.
In experiment of the potentiometer wire of length 100 cm has a resistance of 10, 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 of length 100 cm has a resistance of 10, 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?
The function is
For such questions, we should check the rules of increasing and decreasing function.
The function is
For such questions, we should check the rules of increasing and decreasing function.
If the function is decreasing in its domain then
If the function is decreasing in its domain then
The function is
We have to see the rules for a increasing and decreasing function.
The function is
We have to see the rules for a increasing and decreasing function.