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 f(x) =
 \begin{cases}
 x^2+1 & x > 1 \\
 ax + b & x \le 1
 \end{cases}

Make it continuous and differentiable

Continuous Edit

Make a and be so that at x=1, y=2

2=a+b

Differentiable Edit

\lim_{x \to 1^-} f'(x) = \lim_{x \to 1^+} f'(x)


a = 2x


a = 2

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