91Ó°ÊÓ

For the following exercises, use a calculator to approximate local minima and maxima or the global minimum and maximum. $$ f(x)=x^{3}-x-1 $$

For the following exercises, use a calculator to approximate local minima and maxima or the global minimum and maximum. $$ f(x)=2 x^{3}-3 x-1 $$

For the following exercises, use a calculator to approximate local minima and maxima or the global minimum and maximum. $$ f(x)=x^{4}+x $$

For the following exercises, use a calculator to approximate local minima and maxima or the global minimum and maximum. $$ f(x)=-x^{4}+3 x-2 $$

For the following exercises, use a calculator to approximate local minima and maxima or the global minimum and maximum. $$ f(x)=x^{4}-x^{3}+1 $$

For the following exercises, write the polynomial function that models the given situation. A rectangle has a length of 10 units and a width of \(x\) by \(x\) units are cut out of each comer, and then the sides are folded up to create an open box. Express the box as a polynomial function in terms of \(x\) .

For the following exercises, write the polynomial function that models the given situation. A square has sides of 12 units. Squares \(x+1\) by \(x+1\) units are cut out of each comer, and then the sides are folded up to create an open box. Express the volume of the box as a function in terms of \(x\) .

For the following exercises, write the polynomial function that models the given situation. A cylinder has a radius of \(x+2\) units and a height of 3 units greater. Expres of the cylinder as a polynomial function.

For the following exercises, write the polynomial function that models the given situation. A right circular cone has a radius of \(3 x+6\) and a height 3 units less. Express the volume of the cone as a polynomial function. The volume of a cone is \(V=\frac{1}{3} \pi r^{2} h\) for radius \(r\) and height \(h\)

If division of a polynomial by a binomial results in a remainder of zero, what can be conclude?