If f(x) =x(x+1)(x-4), use interval notation to give all values of x where f(x) >0?

Answer 1

Im not sure don't right this at your Homework.........
where f(x) > 0. a. (–3, 1) b . (–3, 0) ∪ (1, ∞) c . (1, 3) d . (0, 1) ∪ (3, ∞) If f(x) = x(x – 1)(x – 4)2, use interval ..............??????


SORRY I DON'T HELP TOO MUCH I TRY MY BEST......

Answer 2

f(x) =x(x+1)(x-4)
f(x) is < 0 for 0< x< 4 and is = 0 for x=0, -1, and 4
Thus the graph of f(x) starts at - infinity rises and crosses the x-axis at X= -1 , reaches a local maximum and then turns downward and passes through the x-axis at x= 0 and contimuus downward until it reaches a local minimum and the rises again and crosses the x=axis at x=4 and continue on upward to + infinity.

Thus f(x) > 0 for -1

Answer 3

look the factors one by one

x>o for x>o ; x+1 >0 for x > -1 x-4>0 for x> +4

so make a table
-infinite -1 0 4
x - - + +
x+1 - + + +
x-4 - - - +

sign - + - +

f(x) >0 for -14
Product

Answer 4

Graph this problem on your calculator. Look at the y values greater than 0. this is your answer.

Answer 5

Are you trying to answer a homework problem?

The answer is:

x = (-1,0); x = (4, infinity]

but do you know why?

I'll leave it to you to figure that part out yourself.
(hint: what are the properties of a cubic function?)

Answer 6

(-1,0)U(4,inf)