# Continuity And Differentiability

1. Jan 10, 2004

### himanshu121

Consider $$f(x)=x^3-x^2+x+1$$
$$g(x)=\left\{\begin{array}{cc}{max\{f(t),0\leq t \leq x\}}\;\ 0\leq x \leq 1 \\ 3-x\;\ 1< x \leq 2\end{array}\right$$

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 ??[?]

Last edited: Jan 10, 2004
2. Jan 10, 2004

### Moni

Oh! I am also in difficulty with "Continuity And Differentiability" like limits! Seems you can explain a little :)

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