Question

What is the sign of f on the interval -5

Answer 1

Answer:

f(x) = x3 - 3x + 1

f'(x) = 3x2 - 3 = 3(x2 - 1) = 3(x+1)(x-1)

Find the critical numbers:  set f'(x) = 0

                                    3(x+1)(x-1) = 0     x = 1, -1

Check the sign of f'(x) on either side of each critical number.  If f'(x) is positive on an interval, then f is increasing on the interval.  If f'(x) is negative on an interval, then f is decreasing on the interval.  

     +      l       -       l      +     sign f'(x)

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            -1              1

f is increasing on (-∞, -1) υ (1, ∞)

f is decreasing on (-1, 1)