Question

 

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

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

Q1

If a < 0, and f (x) = eax + e–ax is monotonically decreasing. Find the interval to which x belongs.   

Q3

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

Q4

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

Q5

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

Q6

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: 

Q7

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

Q8

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

Q9

 

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

 

Q10

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