Application of DerivativeHard
Question
The function 
is monotonically decreasing at the point
is monotonically decreasing at the point Options
A.x = 3
B.x = 1
C.x = 2
D.none of these
Solution
f(x) =
The given function is not differentiable at x = 1
f′(x) =
Now f′(x) < 0 ⇒
f(x) decreasing ∀ x ∈ (0, 1) ∪ (2, ∞) and f(x) increases ∀ x ∈ (-∞ ) ∪ (1, 2)
here f(x) is decreasing at all points in x ∈ (0, 1) ∪ (2, ∞) so will also be decreasing at x = 3
at x = 1 minima and at x = 2 maxima
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