Question 70 of 82intermediate🔧 ApplyLong Answer5 marks

Find the intervals in which the function ff given by f(x)=x3+1x3f(x) = x^3 + \frac{1}{x^3}, x≠0x \neq 0 is

(i)

increasing

Answer

f is increasing in (-∞, -1) and (1, ∞)

(ii)

decreasing

Answer

f is decreasing in (-1, 0) and (0, 1)

Explanation

This question tests understanding of increasing and decreasing functions using derivatives. The student needs to find f′(x)f'(x), determine critical points by solving f′(x)=0f'(x) = 0, divide the domain into intervals, and check the sign of f′(x)f'(x) in each interval. The domain excludes x=0x = 0 where the function is undefined.

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