Question

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

Solution

Correct option is

(x) is monotonically decreasing if x < 0

Given a < 0, and                                                      …(i) 

                   

  

                                          …(ii)

As from (i) a < 0 

Thus, (x) is monotonically decreasing if x < 0.  

SIMILAR QUESTIONS

Q1

The minimum value of 

Q2

Find the interval in which f (x) = 2x3 + 3x2 – 12x + 1 is increasing.

Q3

Find the interval in which (x) = x3 – 3x2 – 9x + 20 is strictly increasing or strictly decreasing.

Q4

 

Find the interval of increase or decrease of the 

                 

Q5

The function (x) = sin4 x + cos4 x increasing if:

Q6

 Then f decreases in the interval   

Q8

Find the interval for which (x) = x – sin x is increasing or decreasing.

Q9

   

Where a is positive constant. Find the interval in which f’ (x) is increasing.