The correct option is (b) x > 4 or x < -1
Explanation: Since f(x) = 2x^3 – 9x^2 – 24x + 5
Therefore, f’(x) = 6x^2 – 18x + 24
= 6(x – 4)(x + 1)
If x > 4, then, x – 4 > 0 and x + 1 > 0
Thus, (x – 4)(x + 1) > 0 i.e., f’(x) > 0, when x > 4
Again, if x < -1, then, x – 4 < 0 and x + 1 < 0
So, from here,
(x – 4)(x + 1) > 0 i.e., f’(x) > 0, when x < -1
Hence, f’(x) > 0, when x > 4 Or x < -1
Therefore, f(x) increases with x when, x > 4 or x < -1