Continuity and Differentiability Test

Result

Continuity and Differentiability Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

The function f (x) = 1 + |sin x| is

A
differentiable everywhere

B
differentiable nowhere

C
continuous nowhere

D
continuous everywhere

Solution

f(x) = 1 + |sinx| is not derivable at those x for which x for which sinx = 0, however, 1 + |sinx| is continuous everywhere (being the sum of two continuous functions)
Question 2
1 / -0

Let f (x) = [x], then f (x) is

A
differentiable for all x ∈ R

B
continuous nowhere

C
differentiable for all x ∈ ( R − I)

D
continuous for all x ∈ R

Solution

f(x) = [x] is derivable at all x except at integral points i.e. on R – I .