Please help me to solve this question as I am not able to understand this - Maths - Continuity and Differentiability

Question

Please help me to solve this question as I am not able to
understand this

Anand Kumar Pandey · Accepted Answer

Solution :

We have:fx=x2x≤2ax+bx>2As fx is differentiable at x=2, hence it must be continuous at x=2
⇒limx→2- fx=limx→2+ fx⇒limx→2- x2=limx→2+ ax+b⇒22=2a+b⇒2a+b=4 ;iDifferentiating fx with respect to x ,we get:f'x=2xx≤2ax>2Again as fx is differentiable at x=2, hence f'x must be continuous at x=2
⇒limx→2- f'x=limx→2+ f'x⇒limx→2- 2x=limx→2+ a⇒2×2=a⇒a=4Put this in i2×4+b=4⇒b=-4Hence a=4 and b=-4
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