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Question:

Let f(x) = 5 - |x - 2| and g(x) = |x + 1|, x ∈ R. If f(x) attains maximum value of α and g(x) attains minimum value at β, then limx→αβ(x - 1)(x² - 5x + 6)/(x² - 6x + 8) is equal to

-3/2

1/2

-1/2

3/2

Solution:

Correct option is A. 1/2
Maxima of f(x) occurred at x = 2 i.e. α = 2
Minima of g(x) occurred at x = -1 i.e. β = -1
∴ limx→2(-1)(x - 1)(x - 2)(x - 3)/(x - 2)(x - 4) = 1/2.