Question

Over what interval is the function in this graph increasing ?

Answer 1

Answer: -4 ≤ x ≤ 1

Step-by-step explanation:

A function f(x) is called increasing in an interval [a,b] when f'(x) > 0 in the interval (a,b).

That is, in that interval, with increasing the value of x the value of f(x) increases.

Let f(x) be the function which is shown in the given diagram.

Since, by the given diagram,

In the interval $(-\infty, -4)$, f(x) decreases as x increases,

Hence In this interval given function is decreasing.

In the interval [-4, 1], f(x) increases as x increases,

Hence In this interval given function is increasing.

In the interval (1,6), f(x) is constant as x increases,

Hence In this interval given function is neither increasing nor decreasing.

In the interval $(6,\infty)$, f(x) decreases as x increases,

Hence In this interval given function is decreasing.