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
Let [x] denote the greatest integer less than or equal to x. If f(x) = [x sin πx], then f(x) is...Let f(x) = x3 and g(x) = | x |. Then at x = 0, the composite functions -...Let f(x) = [x] & g(x) = , then (where [.] denotes greatest integer function) -...A function y = f(x) has second order derivative f″(x) = 6(x - 1). If its graph passes through the point (2, 1) and...If f is differentiable in (0, 6) & f′(4) = 5 then =...