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)

step-by-step explanation:

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,