JEE Mains Model Paper 24

g'(x) = f(x) (By Leibinitx rule)
g'(x) = 0 when 2 - ex−1 = 0 or when x - e = 0
⇒ x = 1 + ln 2 , x = e
At x = 1 + ln 2 , g'' (x) = −ex−1 = −eln2 = -2
∴ Local maxima at x = 1 + ln 2
At x = e , g'' (x) = 1 > 0 ∴ Local minima at x = e