# Continuously Differentiable

1. Dec 9, 2013

### swhww3

1. The problem statement, all variables and given/known data
Given the function:
1, x≤0;
$\phi$={1-3x^2+2x^3, 0<x<1;
0, x≥1.
Show that $\phi$ is continuously differentiable and provide its equation
2. Relevant equations

3. The attempt at a solution
I have figured out that it is continuously differentiable because the limit as x approaches 0 is 1, and as it approaches 1 it is zero; thus there is no discontinuities. However, what would the derivate equation be? Thanks

2. Dec 9, 2013

### tiny-tim

hi swhww3! welcome to pf!
you've only proved that it is continuous
the equation for the derivative will be in three parts, like the original equation