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प्रश्न
Choose the correct alternative:
The function f(x) = x3 – 3x2 + 3x – 100, x ∈ R is
विकल्प
increasing for all x ∈ R, x ≠ 1
decreasing
neither increasing nor decreasing
decreasing for all x ∈ R, x ≠ 1
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उत्तर
increasing for all x ∈ R, x ≠ 1
संबंधित प्रश्न
Show that the function `f(x) = x^3 - 3x^2 + 6x - 100` is increasing on R
Find the intervals in which the function f given by f(x) = 2x2 − 3x is
- strictly increasing
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(ii) strictly increasing in (π, 2π)
(iii) neither increasing nor decreasing in (0, 2π).
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If f'(x) > 0 for all x ∈ (a, b) then f(x) is decreasing function in the interval (a, b).
Find the value of x for which the function f(x)= 2x3 – 9x2 + 12x + 2 is decreasing.
Given f(x) = 2x3 – 9x2 + 12x + 2
∴ f'(x) = `squarex^2 - square + square`
∴ f'(x) = `6(x - 1)(square)`
Now f'(x) < 0
∴ 6(x – 1)(x – 2) < 0
Since ab < 0 ⇔a < 0 and b < 0 or a > 0 and b < 0
Case 1: (x – 1) < 0 and (x – 2) < 0
∴ x < `square` and x > `square`
Which is contradiction
Case 2: x – 1 and x – 2 < 0
∴ x > `square` and x < `square`
1 < `square` < 2
f(x) is decreasing if and only if x ∈ `square`
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