A) f (x) has local maximum at x = 1
B) f (x) has point of inflexion at x = 1
C) f (x) has local minimum at x = 2
D) all of these
Correct Answer: A
Solution :
\[f(x)={{(x-1)}^{2}}{{(x-2)}^{3}}{{e}^{x}}\] \[\Rightarrow \]\[f'(x)=(x-1){{(x-2)}^{2}}({{x}^{2}}+2x-5){{e}^{x}}\]f(x) has local maximum at x = 1, since f'(x) changes from positive to negative. f(x) has a point of inflexion at x = 2.
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