Continuity and DifferentiabilityHard
Question
If f(x) = x(√x + 
then
thenOptions
A.f(x) is continuous but not differentiable at x = 0
B.f(x) is differentiable at x = 0
C.f(x) is not differentiable at x = 0
D.None of the above
Solution
Given, f(x) = x(√x +
⇒ f(x) would exists when x ≥ 0 and x + 1 ≥ 0
⇒ f(x) would exists when x ≥ 0
∴ f(x) is not continuous at x = 0, because LHL does not exist.
Hence, option (c) is correct.
⇒ f(x) would exists when x ≥ 0 and x + 1 ≥ 0
⇒ f(x) would exists when x ≥ 0
∴ f(x) is not continuous at x = 0, because LHL does not exist.
Hence, option (c) is correct.
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