Problem $7$

Let gradf$=0011$ ofhotk?

$f(x,y)=3x^4+3x^{2}y-y^3-3.$

Which of the following statements is not true?

$($a$)f$ has a critical point at $(0,0)$

$($b$)f$ attains a local min at $(\frac{1}{2},-\frac{1}{2}).$

$6$

$($c$)f$ attains a local min at $(-\frac{1}{2},-\frac{1}{2}).$

$($d$)f$ attains a saddle point at $(-1,1).$

$($e$)$ When $y$ is implicitly defined by $f(x,y)=0,$ the rate of change $d\frac{y}{d}x$ at $(1,0)$ is equal to $-4.(0)$

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