The point M (x, y) of the graph of the function y = e –|x| so that area bounded by the tangent at M and the coordinate axes is greatest is -
Text Solution
Verified by ExpertsA
For x ≥ 0, y = e –x . The equation of tangent is Y – y = – e –x
(X – x). This will intersect coordinate axes at (x + ye x , 0) and (0, y + xe –x ). Hence the area of the required triangle A is 
(y + xe –x ) (x + ye x )
= 
(1 + x) 2 e –x [ y = e –x ]
Now 
= 
[– (1 + x) 2 e –x + 2(1 + x)e –x ]
= 
(1 + x) e –x (1 – x)
Note that 
= 0 ⇒ x = 1, –1
Also, 
> 0, if 0 ≤ x < 1 and 
< 0 if x < 1. Hence A is maximum when x = 1 so
y = e –1 . Since y is even function other possibility of M is
(–1, e –1 ).
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