For what value of t is the tangent to the cur | vedclass

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Question

(A) tangent is perpendicular to the $x$-axis if its slope is undefined,which occurs when $\frac{dx}{dt} = 0$ and $\frac{dy}{dt} 
eq 0$.Given the para

Vedclass · Accepted Answer

$t = 0$

Vedclass · Answer

(A) tangent is perpendicular to the $x$-axis if its slope is undefined,which occurs when $\frac{dx}{dt} = 0$ and $\frac{dy}{dt} 
eq 0$.Given the parametric equations $x = t^2 - 1$ and $y = t^2 - t$.We calculate the derivative of $x$ with respect to $t$:$\frac{dx}{dt} = \frac{d}{dt}(t^2 - 1) = 2t$.Setting $\frac{dx}{dt} = 0$ gives $2t = 0$,which implies $t = 0$.At $t = 0$,we check $\frac{dy}{dt} = \frac{d}{dt}(t^2 - t) = 2t - 1$. Substituting $t = 0$,we get $\frac{dy}{dt} = -1 
eq 0$.Since $\frac{dx}{dt} = 0$ and $\frac{dy}{dt} 
eq 0$ at $t = 0$,the tangent is perpendicular to the $x$-axis at $t = 0$.

For what value of $t$ is the tangent to the curve $x = t^2 - 1, y = t^2 - t$ perpendicular to the $x$-axis?

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