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y-x-3-3-2x-2-3x-maximum-minimum-




Question Number 12562 by @ANTARES_VY last updated on 25/Apr/17
y=−(x^3 /3)+2x^2 −3x  maximum−minimum=?
$$\boldsymbol{\mathrm{y}}=−\frac{\boldsymbol{\mathrm{x}}^{\mathrm{3}} }{\mathrm{3}}+\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{\mathrm{x}} \\ $$$$\boldsymbol{\mathrm{maximum}}−\boldsymbol{\mathrm{minimum}}=? \\ $$
Commented by sandy_suhendra last updated on 25/Apr/17
do you mean ”max stationary” and ”min stationary” ?
$$\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:''\mathrm{max}\:\mathrm{stationary}''\:\mathrm{and}\:''\mathrm{min}\:\mathrm{stationary}''\:? \\ $$
Answered by mrW1 last updated on 25/Apr/17
y=−(x/3)(x^2 −6x+9)=−(x/3)(x−3)^2   y_(min) →−∞ with x→+∞  y_(max) →+∞ with x→−∞    maximum−minimum→∞
$${y}=−\frac{{x}}{\mathrm{3}}\left({x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{9}\right)=−\frac{{x}}{\mathrm{3}}\left({x}−\mathrm{3}\right)^{\mathrm{2}} \\ $$$${y}_{{min}} \rightarrow−\infty\:{with}\:{x}\rightarrow+\infty \\ $$$${y}_{{max}} \rightarrow+\infty\:{with}\:{x}\rightarrow−\infty \\ $$$$ \\ $$$$\boldsymbol{\mathrm{maximum}}−\boldsymbol{\mathrm{minimum}}\rightarrow\infty \\ $$

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