Q. 6 A3.8( 30 Votes )

Find the intervals in which the following functions are strictly increasing or decreasing:

x2 + 2x – 5

Answer :

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.


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