What is the derivative equation for a continuously differentiable function?

[swhww3]

Homework Statement

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

Homework Equations

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

 

[tiny-tim]

hi swhww3! welcome to pf!

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.

you've only proved that it is continuous

However, what would the derivate equation be?

the equation for the derivative will be in three parts, like the original equation