91Ó°ÊÓ

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

Raise each complex number to the fourth power. (a) 2 (b) -2 (c) \(2 i\) (d) \(-2 i\)

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

Perform the division by assuming that \(n\) is a positive integer. \(\frac{x^{3 n}+9 x^{2 n}+27 x^{n}+27}{x^{n}+3}\)

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. \(g(x)=\frac{1}{5}(x+1)^{2}(x-3)(2 x-9)\)

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. \(f(x)=4 x^{3}-3 x^{2}+2 x-1\)

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

Perform the division by assuming that \(n\) is a positive integer. \(\frac{x^{3 n}-3 x^{2 n}+5 x^{n}-6}{x^{n}-2}\)

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. \(h(x)=\frac{1}{5}(x+2)^{2}(3 x-5)^{2}\)

Write each of the powers of \(i\) as \(i,-i, 1,\) or -1 . (a) \(i^{40}\) (b) \(i^{25}\) (c) \(i^{50}\) (d) \(i^{67}\)