Answer:
For x < -2 f(x) < 0.
For 5 < x < 7 , f(x) < 0.
In interval notation it is:
(∞, -2) ∪ ( 5, 7).
Step-by-step explanation:
First find the critical values of x:
f(x) = (x - 5)(x + 2)(x - 7) = 0
x = 5, -2 and 7.
(x - 5)(x + 2)(x - 7) < 0
Consider x = -2:
When x < -2 the sign of the expression is - * - * - = -
and it is 0 for x = -2
So for x < -2, f(x) < 0.
For:
-2 < x < 5 the sign of f(x) is - * + * - = +
So for -2 < x < 5, f(x) > 0
For:
5 < x < 7 the sign of f(x) is + * + * - = -
So for 5 < x < 7 , f(x) < 0.
For x > 7, f(x) > 0.
