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in Derivatives by (49.2k points)
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The function f(x) = x3 - 27x+8 is increasing when

A. |x| < 3

B. |x| > 3

C. -3 < x < 3

D. none of these

1 Answer

+1 vote
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Best answer

Answer is : B. |x| > 3

Given:

f(x) = x- 27x+8.

f’(x) = 3x- 27x = 0

f’(x) = 3(x- 9) = 0

f’(x) = 3(x -3)(x+3) = 0

x = 3 or x = -3

for x>3 f(x) is increasing

for x3 f(x) is increasing.

∴ for |x|>3 f(x) is increasing.

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