Find the Maximum Number of Real Roots f(x)=6x-x^3

$f (x) = 6 x - x^{3}$

Step 1

Reorder $6 x$ and $- x^{3}$ .

$f (x) = - x^{3} + 6 x$

Step 2

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$- x^{3} \to 3$

$6 x \to 1$

Step 3

The largest exponent is the degree of the polynomial.

$3$

Step 4

The maximum number of possible roots is the degree of $- x^{3} + 6 x$ .

$3$