Extrema of a Parametric Path

Question

The path of a particle is given by the parametric equations $$x(t) = t^2 - 4*t + 3$$ and $$y(t) = -t^2 + 4*t + 1$$. Which of the following statements is true regarding the horizontal and vertical extrema of the particle's path?

Accepted Answer

The particle attains its horizontal minimum of $$-1$$ and vertical maximum of $$5$$ at $$t=2$$.

Answer

The particle attains its horizontal minimum of $$-1$$ at $$t=2$$, but the vertical function has no maximum.

Answer

The particle's horizontal and vertical extrema occur at different values of $$t$$.

Answer

The particle attains its horizontal maximum of $$-1$$ and vertical minimum of $$5$$ at $$t=2$$.

Extrema of a Parametric Path

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