91Ó°ÊÓ

A function with the parameters \(a\) and \(b\) are given. Describe the critical points and possible points of inflection of \(f\) in terms of \(a\) and \(b\). \(f(x)=(x-a)(x-b)\)

A function \(f(x)\) is given. Find the critical points of \(f\) and use the Second Derivative Test, when possible, to determine the relative extrema. \(f(x)=x^{3}-x+1\)

A function \(f(x)\) is given. Find the critical points of \(f\) and use the Second Derivative Test, when possible, to determine the relative extrema. \(f(x)=2 x^{3}-3 x^{2}+9 x+5\)

A function \(f(x)\) is given. Find the critical points of \(f\) and use the Second Derivative Test, when possible, to determine the relative extrema. \(f(x)=\frac{x^{4}}{4}+\frac{x^{3}}{3}-2 x+3\)

A function \(f(x)\) is given. Find the critical points of \(f\) and use the Second Derivative Test, when possible, to determine the relative extrema. . \(f(x)=-3 x^{4}+8 x^{3}+6 x^{2}-24 x+2\)

A function \(f(x)\) is given. Find the critical points of \(f\) and use the Second Derivative Test, when possible, to determine the relative extrema. \(f(x)=x^{4}-4 x^{3}+6 x^{2}-4 x+1\)

A function \(f(x)\) is given. Find the critical points of \(f\) and use the Second Derivative Test, when possible, to determine the relative extrema. \(f(x)=\sec x\) on \((-3 \pi / 2,3 \pi / 2)\)

A function \(f(x)\) is given. Find the critical points of \(f\) and use the Second Derivative Test, when possible, to determine the relative extrema. \(f(x)=\frac{1}{x^{2}+1}\)

A function \(f(x)\) is given. Find the critical points of \(f\) and use the Second Derivative Test, when possible, to determine the relative extrema. \(f(x)=\frac{x}{x^{2}-1}\)

A function \(f(x)\) is given. Find the critical points of \(f\) and use the Second Derivative Test, when possible, to determine the relative extrema. \(f(x)=\sin x+\cos x\) on \((-\pi, \pi)\)