Perform the Following for the Function Defined By $f(x)=2 x^{4}+x^{3}-13 x^{2}-5 x+15$

Essay

Perform the following for the function defined by $f(x)=2 x^{4}+x^{3}-13 x^{2}-5 x+15$ .
(a) List all possible rational zeros.
(b) Find all rational zeros.
(c) Use the intermediate value theorem to show that there must be a zero between 2 and 3.
(d) Use Descartes' rule of signs to determine the possible number of positive zeros and negative zeros.
(e) Use the boundedness theorem to show that there is no zero less than -3 and no zero greater than 3 .