Find the intervals in which the following functions are strictly increasing or decreasing:
x2 + 2x – 5
It is given that function f(x) = x2 + 2x – 5
f’(x) = 2x + 2
If f’(x) = 0, then we get,
⇒ x = -1
So, the point x = -1 divides the real line into two disjoint intervals, (-∞,-1) and (1,∞)
So, in interval (-∞,-1)
f’(x) = 2x + 2 < 0
Therefore, the given function (f) is strictly decreasing in interval (-∞,-1).
And in interval (1,∞)
f’(x) = 2x + 2 > 0
Therefore, the given function (f) is strictly increasing in interval (1,∞).
Thus, f is strictly increasing for x > -1.