What's the domain of g(x)=9x-11x^4

Question

Find the domain of g(x)=9x-11x^4 and the range of it.

Answer 1

It's a polynomial, isn't it?

 

The domain of EVERY polynomial is all Reals.

To find the range, examine its graph.

Answer 2

The domain is all Real Numbers.

 

Calculating the zeros: (9 - 11x^3)x=0

 

             x= 0 and x^3 = 9/11

 

            x=0 and x = cube root (9/11) = 0.9353.....

 

Setting up a sign chart, the intervals of interest are:

  x<0,   0 < x < cube root(9/11),   x>cube root(9/11)

 

This function is positive only when 0 < x < cube root(9/11)

 

Without using calculus, the max must be found numerically.

It is y = 3.977 when x= 0.589 

 

 

Examining the graph at desmos.com is the best way to find these results.