Continuity and DifferentiabilityHard
Question
Let f : R → R be a function defined by f(x) = max {x, x3} The set of all points ehere f(x) is not differentiable, is
Options
A.{-1,1}
B.{-1,0}
C.{0,1}
D.{-1,0,1}
Solution
Given f(x) ax {x, x3} considering the graph separately,
y = x3 and y = x
Note y = x3 is odd order parabola and y = x is always intersect at (1, 1) and (-1, -1)
Now
⇒ f′(x)
The point of consideration are
f′(-1-)= 1 and f′(-1+) = 3
f′(-0-) = 0 and f′(0+) = 1
f′(1-) = 1 and f′(1+) = 3
Hence, f is not differentiable at -1,0,1.
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