Perform the Following for the Function Defined By $f(x)=3 x^{4}-8 x^{3}-6 x^{2}+17 x+6$

Essay

Perform the following for the function defined by $f(x)=3 x^{4}-8 x^{3}-6 x^{2}+17 x+6$ .
(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 -1 .
(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 -2 and no zero greater than 4 .