What is the sign of f on the interval -5

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)

            -1              1

f is increasing on (-∞, -1) υ (1, ∞)

f is decreasing on (-1, 1)

19.

step-by-step explanation:

you add the 9 in the tens column since it is a single digit and 9 plus zero is 9 so it is 19

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.