Question

Give the interval(s) on which the function f is positive if f is defined as:

f(x)=x(5−x)(2x−3)

Answer 1

Try writing it as

f(x) = -x(x-5)(2x-3)

Now you can see that the coefficient of x^3 is negative.

So, for x very large negative, say, -100, f(x) is positive. So, the graph comes down on the left, crosses the x axis at 0,3/2,5, and then continues on down to the right.

So, f(x) > 0 on (-∞,0)U(3/2,5)