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.
Create a free account to view solution
View Solution FreeMore Continuity and Differentiability Questions
The value(s) of x for which f(x) = is continuous, is (are) -...If y = f(x) is an odd differentiable function defined on (-∞, ∞) such tha f′(3) = -2, then f′(-3...The set of all point where the function f(x) = 2x |x| is differentiable is -...If (x) = , g(x) = and h(x) = 2x - 3, then f′(h′(g′(x)) =...Identify the correct statement -...