Question

   

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

Solution

Correct option is

f’(x) decreases on  and increase on 

 

Differentiating both sides, we have

                        

Again differentiating both sides, we have

                        

Now f’’(x) =  0 then in the interval x ≤ 0 the root is 

And in interval when x > 0 root is   

Using sign scheme or number line rule, as shown in fig.     

Hence, f’(x) decreases on  and increase on 

SIMILAR QUESTIONS

Q1

Let (x) be a function such that f’(a≠ 0. Then at x = α ; f (x)

Q2

The minimum value of 

Q3

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

Q4

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

Q5

 

Find the interval of increase or decrease of the 

                 

Q6

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

Q7

 Then f decreases in the interval   

Q9

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

Q10

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