differentiating to find one unknown function out of three?? 1. The problem statement, all variables and given/known data Hi everyone I need some help with a question that i have solved yet i find it hard to understand. I have three given functions in the picture attached. All three consist of one single graph. And they give me the functions for two parts whereas i have to find out the last one which is the parable. 2. Relevant equations I needed to differentiate what i already had given, since i wanted to find the slope of the functions since i also know that where one function stops and the other begins i have the same slope. 3. The attempt at a solution I tried to solve it by saying that g(x)=ax^2+bx+c then i differentiate it and it becomes: g'(x)=2ax+b i now look at the first function f(x)=-1 is f^' (x)=0 this means that the slope for this function is 0. the slope for the points (-2;0) must therefore also be 0. i put this in the parable function g'(x)=2ax+b g'(-2)=-4a+b=0 then i know that in the points (0;0) the slope of the parable must be the same as the one for h(x) i have to find h'(0) and it wont work unless i get it to be h'(0)=1=b but i dont get 1 since i say h'(0)=0,006*0^2-0,18 h'(0)=-0,18 the end result should be g(x) = 1/4 x + x what is wrong where i stop up ? can someone please tell my why i wont get it right..