Question

The value 3 is an upper bound for the zeros of the function shown below.

ƒ(x)=-3x^3+20x^2-36x+16

True or false

Answer 1

Start by factoring
\[-3x^3+20x^2-36x+16 = - \left( x-2 \right) \left( x-4 \right) \left( 3\,x-2 \right) \]

Answer 2

Look at each root and see if 3 is an upper bound for those roots

Answer 3

The answer is no since 4 is a root and 4 is greater than 3.

Answer 4

\[x \in [2, 4, \frac{2}{3}]\]