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What will be the range of the function f(x) = 2x3 – 9x2 – 24x + 5 which decreases with x?

What will be the range of the function f(x) = 2x3 – 9x2 – 24x + 5 which decreases with x? Correct Answer -1 < x < 4

Since f(x) = 2x3 – 9x2 – 24x + 5 Therefore, f’(x) = 6x2 – 18x + 24 = 6(x – 4)(x + 1) If -1 < x < 4, then x – 4 < 0 and x + 1 > 0 Thus, (x – 4)(x + 1) < 0 i.e., f’(x) < 0, when -1 < x < 4 Therefore, f(x) decreases with x, when, -1 < x < 4.

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