The function f (x) = (x2 – 1) |x2 – 3x +2| + cos ( | x | ) is not differentiable at
The function f (x) = (x2 – 1) |x2 – 3x +2| + cos (|x|) …(i)
Here, | x | is not differentiable at x = 0 but
∴ cos (|x|) is differentiable at x = 0 …(ii)
Now, to check differentiability at x = 1, 2 (using shortcut method)
Thus, for f ' (1) we have
Thus f (x) is differentiable at x = 1
Thus, f (x) is not differentiable at x = 2
for what value of k, f (x) is continuous at x = 0?
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, then draw the graph of f (x) in the interval [–2, 2] and discuss the continuity and differentiability in [–2, 2]
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