91Ó°ÊÓ

Use a graphing utility to graph the function. Use the zero or root feature to approximate the real zeros of the function. Then determine the multiplicity of each zero. $$f(x)=x^{3}-16 x$$

Find the values of \(\boldsymbol{b}\) such that the function has the given maximum or minimum value. $$f(x)=-x^{2}+b x-75 ; \text { Maximum value: } 25$$

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$h(x)=2 x^{4}-3 x+2$$

Determine whether the statement is true or false. Justify your answer. The equation $$\frac{x^{3}-3 x^{2}+4}{x+1}=x^{2}-4 x+4$$ is true for all values of \(x .\)

Simplify the complex number and write it in standard form. $$(-i)^{6}$$

Use a graphing utility to graph the function. Use the zero or root feature to approximate the real zeros of the function. Then determine the multiplicity of each zero. $$f(x)=\frac{1}{4} x^{4}-2 x^{2}$$

Find the values of \(\boldsymbol{b}\) such that the function has the given maximum or minimum value. $$f(x)=-x^{2}+b x-16 ; \text { Maximum value: } 48$$

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$g(x)=5 x^{5}-10 x$$

Find the values of \(\boldsymbol{b}\) such that the function has the given maximum or minimum value. $$f(x)=x^{2}+b x+26 ; \text { Minimum value: } 10$$

Use a graphing utility to graph the function. Use the zero or root feature to approximate the real zeros of the function. Then determine the multiplicity of each zero. $$g(x)=\frac{1}{5}(x+1)^{2}(x-3)(2 x-9)$$