Consider f(x)= cases A(x-1)^ 2 +B(x-1)+3,&x 1 x + C,&x>1 cases Find ,

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Consider

f(x)=\begin{cases}A(x-1)^{2}+B(x-1)+3,&x\le 1\\ \ln x + C,&x>1\end{cases}

Find

A

,

B

, and

C

so that

f

,

f'

, and

f''

are all continuous at

x=1

.

Related theory

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