The derivative f'(x) can be written by the graph as shown below:
Now integrate each piece as follows;
[tex]\begin{gathered} \text{ For 0}\leq x<1,\text{ f(x)=2x+c}\ldots(i) \\ \text{For 1}It is also given that f(0)=-1
So 2(0)+c=-1 which implies that c=-1
So the function becomes:
The graph is shown below:
