Continuity and DifferentiabilityHard
Question
If f(x) = 3 (2x + 3)2/3 + 2x + 3 then -
Options
A.f(x) is continuous but not differentiable at x = -3/2
B.f(x) is differentiable at x = 0
C.f(x) is continuous at x = 0
D.f(x) is differentiable but not continuous at x = -3/2
Solution
f(x) = 3(2x + 3)2/3 + 2x + 3
f′(x) =
+ 2
Now 2x + 3 ≠ 0 ⇒ x ≠
Hence f’(x) is continuous but not differentiable at x = - 3/2
Also f(x) is differentiable & continuous at x = 0
f′(x) =
+ 2Now 2x + 3 ≠ 0 ⇒ x ≠
Hence f’(x) is continuous but not differentiable at x = - 3/2
Also f(x) is differentiable & continuous at x = 0
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