Bellow is an apple to introduce you to what finding the derivative of a function will look like graphically.

Above is a linear function, grab point a and drag it alone the function, the derivative of the function will be traced your goal is to tell me the type of function that was traced and what the equation might be.
1.) What type of equation is the derivative? What is the equation?
2.) Input the new equation f(x) = x^2 - 4. What type of equation is the derivative? What is the equation?
3.) Input the new equation f(x) = 3x^3 - 4x. What type of equation is the derivative? What is the equation?
4.) What type of graph might the derivative of the function f(x) = 4x^6 +3x^2 + 5x - 6 produce.