A) \[3x+4y=16\]
B) \[4x+y=4\]
C) \[x+y=4\]
D) \[4x-3y=-12\]
E) \[x-y=-4\]
Correct Answer: C
Solution :
As the curve crosses\[y-\]axis ie,\[x=0\] \[\therefore \] \[y=4{{e}^{-0}}\Rightarrow y=4\] Given, \[y=4{{e}^{-\frac{x}{4}}}\] \[\Rightarrow \] \[\frac{dy}{dx}=4{{e}^{-\frac{x}{4}}}\left( -\frac{1}{4} \right)=-{{e}^{-\frac{x}{4}}}\] \[\Rightarrow \] \[{{\left( \frac{dy}{dx} \right)}_{(0,4)}}=-{{e}^{-0}}=-1\] \[\therefore \]Equation of tangent at (0, 4) is \[y-4=-1(x-0)\] \[\Rightarrow \] \[x+y=4\]You need to login to perform this action.
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