Application of DerivativeHard

Question

The line = 1 touches the curve y = be-x/a at the point

Options

A.(- a, 2b)
B.
C.
D.(0, b)

Solution

   
= 1 -
= e-x/a
⇒     e-x/a = 1 -
put t = -
et  = 1 + t
Draw graph of y = et,    y = 1 + t
From graph it is clear that t = 0 is the only solution
⇒    x = 0        ⇒    y = b        (0, b)

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