Question

Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work. (Enter your answers as a comma-separated list of ordered pairs.) $x = t^3 - 3t$, $y = t^2 - 5$ horizontal tangent $(x, y) =$ vertical tangent $(x, y) = $

          Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work. (Enter your answers as a comma-separated list of ordered pairs.)
$x = t^3 - 3t$, $y = t^2 - 5$
horizontal tangent $(x, y) =$
vertical tangent $(x, y) = $

Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing device, graph the curve to check your work. (Enter your answers as a comma-separated list of ordered pairs.)
x = t^3 - 3t, y = t^2 - 5
horizontal tangent (x, y) =
vertical tangent (x, y) =

Added by Pilar G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

06/21/2022

Step 1

Step 1:** Calculate the derivative of y with respect to x for the parametric curve: \[ \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{2t}{3t^2 - 3} = \frac{2t}{3(t^2 - 1)} = \frac{2t}{3}(t - 1)(t + 1) \] ** Show more…

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