Question

Which is the interval where the function f(x) = -| x + 3 | - 2 is increasing?

x < -3

x < -3

x > -3

x > -3

Answer 1

Explanation:

If f

′

(x)>0 at each point in an interval I, then the function is said to be increasing on I. f

′

(x)<0 at each point in an interval I, then the function is said to be decreasing on I.

f(x)=x

3

−3x

f

′

(x)=3x

2

−3

Increasing:

when 3x

2

−3>0

i.e. x

2

>1

⟹xϵ(−∞,−1)∪(1,∞)

Decreasing:

when 3x

2

−3<0

i.e. x

2

<1

⟹xϵ(−1,1)