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Question

If f(x)=⎪ ⎪ ⎪⎪ ⎪ ⎪x29x3+α, for x>35, for x=32x2+3x+β, for x<3
is continuous at x=3, find α and β.

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Solution

For x>3, f(x)=x29x3+α=x+3+α

For x=3, f(x)=5

For x<3, f(x)=2x2+3x+β

Now, for continuity at x=3,

f(3)=f(3)=f(3+)

2(3)2+3(3)+β=5=3+3+α

27+β=5=6+α

α=1 and β=22

This is the required solution

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