Value of x of which a slope is undefined for a parametric graph.

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Answer was x=8, question incorrectly marked.

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User114
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User114

Updated on April 06, 2020

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  • User114
    User114 over 2 years

    For what values of $x$ is the slope undefined for the graph

    $$x=8-t^3$$

    $$y=t^2-6t$$

    The slope should be undefined when $\frac {dx}{dt}=0$.

    $$\frac {dx}{dt}=-3 t^2$$

    $$-3t^2=0$$

    $$t=0$$

    When $t=0$, $x=8$ so the $x$ value should be $8$, but the question was marked incorrect. What is incorrect in this?

    • Mufasa
      Mufasa over 7 years
      Slope is undefiend when $\frac{dy}{dx}=\infty$. Note:$$\frac{dy}{dx}=\frac{dy}{dt}\div\frac{dx}{dt}$$
    • Mufasa
      Mufasa over 7 years
      Yes - you are right
    • Mufasa
      Mufasa over 7 years
      Yes - assuming you have indeed stated the question correctly
    • Mufasa
      Mufasa over 7 years
      Then I agree - they marked your answer wrong incorrectly.
    • Prasun Biswas
      Prasun Biswas over 7 years
      @Mufasa, I disagree with your first comment. What if the slope is $-\tan\left(\dfrac{\pi}{2}\right)$ ? It should be $\dfrac{dx}{dy}=0$ for the slope to be undefined. This covers both the undefined slopes $\tan\left(\pm\dfrac{\pi}{2}\right)$
    • Mufasa
      Mufasa over 7 years
      @PrasunBiswas - my mistake, I should have stated slope is undefined when:$$\frac{dy}{dx}=\pm\infty$$Thanks for pointing it out.