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A curve has parametric equations x=2t-ln2t and y=t²-ln t² where t>0. Find the value of t at the point on the curve where dy/dx =2 . Hence ,find the coordinates of that point?

1 Answer

Aug 30, 2015

Coordinates of the point would be x=4-ln4 and y= 4-ln4

Explanation:

$\frac{d x}{d t} = 2 - \frac{1}{t} and \frac{d y}{d t} = 2 t - \frac{2}{t}$ $dx/dt=2-1/t and dy/dt= 2t-2/t$

Since $\frac{d y}{d x} = 2$ $dy/dx=2$ , $2 - \frac{1}{t} = t - \frac{1}{t}$ $2-1/t=t-1/t$ . That gives t=2.

Hence coordinates of the point would be x=4-ln4 and y= 4-ln4

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