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Shape of a function (with convexity)
Task number: 3049
Investigate the shape of the following functions including their asymptotes, limits at boundary points of the domain of definition, and convexity. Sketch their graphs.
Variant 1
f(x)=x3−12x+16
Variant 2
\displaystyle f(x)=\arcsin(\cos x)
Variant 3
\displaystyle f(x)=\ln^3(x)
Variant 4
\displaystyle f(x)=e^{-x^2}
Variant 5
\displaystyle f(x)=\ln(4{\cdot}3^x + 2)
Variant 6
\displaystyle f(x)=\ln\left(\left|\tan\frac{x}4\right|\right)
Variant 7
\displaystyle f(x)=\arcsin\left(\frac{2x}{x^2 + 1}\right)
Variant 8
\displaystyle f(x)=x^2 e^{-x}
Variant 9
\displaystyle f(x)=\frac{x^3}{(x-2)^2}
Variant 10
\displaystyle f(x)=x-\ln(x+1)
Variant 11
\displaystyle f(x)=x\, e^{-|x-1|}