Question

Discuss the continuity and differentiability at x=0

Answer 1

Answer:

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Step-by-step explanation:

f(x)={ x2+1,x≤0 x3,x>0 . Then Differentiability of function f(x) at x=0

Try: As we know that If function f(x) is Differentiable at x=0. Then it must be

continuous at x=0.

⇒f′(x)={ 2x,x≤0 3x3,x>0

⇒f′(0)={ 0,x≤0 0,x>0

⇒ Function f(x) is Differentiable at x=0

So it must be continuous at x=0

But From Question

⇒f(x)={ x2+1,x≤0 x3,x>0

⇒f(0)={ 1,x≤0 0,x>0

Here left side limit and Right side limit are not equal.

So it is not Continuous at x=0

Could some explain me why this is happen.