1 Calculus I

1. Plot $y^3=6x^2-x^3$ following class procedures¹²³. [1, Maximum and Minimum Values, Curve Sketching]
2. Plot $y=(x+1)/x^2$ following class procedures¹². [1, Maximum and Minimum Values, Curve Sketching]
3. Plot $y=\ln(e^{x+1}-1)$ following class procedures¹². [1, Maximum and Minimum Values, Curve Sketching]

¹ Include a plot

² Discuss intercepts, extents, symmetries, asymptotes, asymptotic behavior for $x\to\pm\infty$, local/global maxima/minima, concavity, inflection points, poles, cusps, corners, and other singularities

³ Note that $\lim_{x\to\infty}=\lim_{u\downarrow0}$ if $u=1/x$. Alternatively, use the Taylor series approximation $(1+\varepsilon)^p\sim1+p\varepsilon$ for $\varepsilon\to0$