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Question

The function
f(x)=5x4for 0<x14x23xfor 1<x<23x+4for x2 is

A
Continuous at x=1 and x=2
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B
Continuous at x=1 but not differentiable at x=2
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C
Continuous at x=2 but not differentiable at x=1
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D
Continuous at x=1,x=2 but not differentiable at x=1,x=2.
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Solution

The correct option is B Continuous at x=1 but not differentiable at x=2
f(x)=5x4for 0<x14x23xfor 1<x<23x+4for x2

f(1)=1; f(1+)=1; f(1)=1
f(2)=10; f(2+)=10; f(2)=10
Thus continuous at x=1,2
Now,
f(x)=5for 0<x18x3for 1<x<23for x2

f(1)=5; f(1+)=5
​​​​​​​f(2)=13; f(2+)=3
Thus non differentiable at x=2

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