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The total cost function for production of articles is given as C = 100 + 600x – 3x^{2}, then the values of x for which the total cost is decreasing is ______

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#### Solution

**x >100**

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**Solution: **f(x) = 2x^{3} – 15x^{2} – 84x – 7

∴ f'(x) = `square`

∴ f'(x) = 6`(square) (square)`

Since f(x) is decreasing function.

∴ f'(x) < 0

**Case 1:** `(square)` > 0 and (x + 2) < 0

∴ x ∈ `square`

**Case 2:** `(square)` < 0 and (x + 2) > 0

∴ x ∈ `square`

∴ f(x) is decreasing function if and only if x ∈ `square`

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∴ f'(x) = `squarex^2 - square + square`

∴ f'(x) = `6(x - 1)(square)`

Now f'(x) < 0

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∴ x < `square` and x > `square`

Which is contradiction

**Case 2:** x – 1 and x – 2 < 0

∴ x > `square` and x < `square`

1 < `square` < 2

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In which one of the following intervals is the function f(x) = x^{3} – 12x increasing?