Value of x of which a slope is undefined for a parametric graph.
1,090
Answer was x=8, question incorrectly marked.
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Author by
User114
Updated on April 06, 2020Comments

User114 over 2 years
For what values of $x$ is the slope undefined for the graph
$$x=8t^3$$
$$y=t^26t$$
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 over 7 yearsSlope is undefiend when $\frac{dy}{dx}=\infty$. Note:$$\frac{dy}{dx}=\frac{dy}{dt}\div\frac{dx}{dt}$$

Mufasa over 7 yearsYes  you are right

Mufasa over 7 yearsYes  assuming you have indeed stated the question correctly

Mufasa over 7 yearsThen I agree  they marked your answer wrong incorrectly.

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 over 7 years@PrasunBiswas  my mistake, I should have stated slope is undefined when:$$\frac{dy}{dx}=\pm\infty$$Thanks for pointing it out.
