A small drone travels in the horizontal plane following the parametric path x(t)=2t+1

MATHEMATICS · Multi-part · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane

Problem

A small drone travels in the horizontal plane following the parametric path

x(t)=2t+1,\qquad y(t)=t^{2}-4t+3,\qquad 0\le t\le 6,

where

x

and

y

are measured in meters and

t

in seconds. (a) Determine the slope

\displaystyle \frac{dy}{dx}

of the path at

t=2

. (b) Find the Cartesian equation of the line tangent to the path at

t=2

. (c) Identify all values of

t

in the given interval for which the drone’s path has a horizontal tangent, and provide the corresponding points in the plane. (d) Identify all values of

t

in the given interval for which the drone’s path has a vertical tangent, and provide the corresponding points in the plane.

Related theory

Parametric Functions
Implicit and parametric differentiation
Derivatives of parametric functions
Continuity and Differentiability

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