Find the interval in which function f(x) = where x ∈ R, is strictly decreasing?

Question

Question

Answer 1

Concept:

If f’(x) > 0 for all x in (a, b), then f is increasing on [a, b].

If f’(x) < 0 for all x in (a, b), then f is decreasing on [a, b].

If f’(x) = 0 for all x in (a, b), then f is constant on [a, b].

Calculation:

Given that,

⇒ f(x) = where x ∈ R

To calculate the critical point

⇒ f’(x) =

⇒ f’(x) = 0

⇒

⇒ x²= 36

⇒ x = ± 6

Draw number line with critical points

Note: we put alternate sign on number line starting from right side with positive sign.

From the number line we can say that

⇒ Interval (- ∞, - 6] ∪ [6, ∞) function f is strictly increasing.

⇒ Interval [-6, 6] function f is strictly decreasing.

In our question interval given [-5, 2] is the right answer because it is subinterval of [-6, 6].