Consider [tex]f(x)=x^3-x^2+x+1 [/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex] g(x)=\left\{\begin{array}{cc}{max\{f(t),0\leq t \leq x\}}\;\ 0\leq x \leq 1

\\ 3-x\;\ 1< x \leq 2\end{array}\right[/tex]

Discuss the continuity and differentiability of g(x) in the interval (0,2)

I know how to do it

As f(x) is increasing function therefore max will be x^3-x^2+x+1.

But

I want to know the problem graphically ??[?]

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# Continuity And Differentiability

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