Where a is positive constant. Find the interval in which f’ (x) is increasing.
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
Let f (x) be a function such that f’(a) ≠ 0. Then at x = α ; f (x)
The minimum value of
Find the interval in which f (x) = 2x3 + 3x2 – 12x + 1 is increasing.
Find the interval in which f (x) = x3 – 3x2 – 9x + 20 is strictly increasing or strictly decreasing.
Find the interval of increase or decrease of the
The function f (x) = sin4 x + cos4 x increasing if:
Then f decreases in the interval
Find the interval for which f (x) = x – sin x is increasing or decreasing.
If a < 0, and f (x) = eax + e–ax is monotonically decreasing. Find the interval to which x belongs.