Question

Using calculus, find the order relation between x and tan-1x when  

Solution

Correct option is

  

Thus (x) is increasing function.

(As, we know x1 ≤ x2 ⇒ f (x­1) ≤ (x2) for increasing function).  

   

Thus, the above is order relation between x and tan-1x.

SIMILAR QUESTIONS

Q2

If (x) = ax3 + bx2 + cx + d where abcd are real numbers and 3b2 < c2, is an increasing cubic function and g(x) = af’ (x) + bf’’ (x) + c2, then

Q3

If f : R  R, (x) is a differentiable bijective function, then which of the following is true?

Q4

If (x) and (x) are two positive and increasing function, then

Q5

If the function y = sin (f (x)) is monotonic for all values of x (where (x) is continuous), then the maximum value of the difference between the maximum and the minimum value of (x), is: 

Q6

 where 0 <x < π then the interval in which g(x) is decreasing is:   

Q7

Find the critical points for f (x) = (x – 2)2/3 (2x + 1).

Q8

 

Find all the values of a for which the function possess critical points.

 

Q9

 

Using calculus, find the order relation between x and tan-1x when x Ïµ [0, ∞). 

Q10

The set of all values of ‘b’ for which the function (x) = (b2 – 3b + 2) (cos2x – sin2x) + (b – 1) x + sin 2 does not possesses stationary points is: