Continuity and DifferentiabilityHard
Question
Let f(x) = 
where [x] denotes the greatest integer function.
Then -
where [x] denotes the greatest integer function. Then -
Options
A.f (x) is continuous and differentiable in 
for all a, provided b = 2
for all a, provided b = 2B.f (x) is continuous and differentiable in if f(a) = 4 , b = 2
if f(a) = 4 , b = 2C.f (x) is continuous and differentiable in if a = 4 and b = 0
if a = 4 and b = 0D.for no choice of a and b, f (x) is differentiable in
Solution
f′(x) = 
Now at x = 0
8(0) - 2 = 2(a) (0) - b ⇒ b = 2 and a ∈ R
Also f(x) is continuous in
Now at x = 0
8(0) - 2 = 2(a) (0) - b ⇒ b = 2 and a ∈ R
Also f(x) is continuous in
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