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Magazine Problem 56
Sketch the curves. Identify clearly any interesting features, including local maximum and minimum points, inflection points, asymptotes, and intercepts. $$ y=x^{5}-5 x^{4}+5 x^{3} $$
Problem 57
Sketch the curves. Identify clearly any interesting features, including local maximum and minimum points, inflection points, asymptotes, and intercepts. $$ y=x^{3}-3 x^{2}-9 x+5 $$
Problem 58
Sketch the curves. Identify clearly any interesting features, including local maximum and minimum points, inflection points, asymptotes, and intercepts. $$ y=(x-1)^{2}(x+3)^{2 / 3} $$
Problem 59
Sketch the curves. Identify clearly any interesting features, including local maximum and minimum points, inflection points, asymptotes, and intercepts. $$ x^{2}+x^{2} y^{2}=a^{2} y^{2}, a>0 $$
Problem 60
Sketch the curves. Identify clearly any interesting features, including local maximum and minimum points, inflection points, asymptotes, and intercepts. $$ y=x e^{x} $$
Problem 61
Sketch the curves. Identify clearly any interesting features, including local maximum and minimum points, inflection points, asymptotes, and intercepts. $$ y=\left(e^{x}+e^{-x}\right) / 2 $$
Problem 62
Sketch the curves. Identify clearly any interesting features, including local maximum and minimum points, inflection points, asymptotes, and intercepts. $$ y=e^{-x} \cos x $$
Problem 63
Sketch the curves. Identify clearly any interesting features, including local maximum and minimum points, inflection points, asymptotes, and intercepts. $$ y=e^{x}-\sin x $$
Problem 64
Sketch the curves. Identify clearly any interesting features, including local maximum and minimum points, inflection points, asymptotes, and intercepts. $$ y=e^{x} / x $$
Problem 65
Sketch the curves. Identify clearly any interesting features, including local maximum and minimum points, inflection points, asymptotes, and intercepts. $$ y=4 x+\sqrt{1-x} $$
