1. What is the gradient of the bottom point of a parabola?
The tangent drawn at the base point of a parabola would be horizontal and therefore its gradient is 0.
2. Is the gradient function of a parabola always a straight line?
Yes. Because the exponent of a parabola is two, its derived or gradient function always has an exponent of one.
i.e. A linear function.
3. What is the gradient function of a linear function?
The gradient function of a linear function will be f(x) = c, where c is a constant.
This is because the gradient of a straight line is constant.
e.g. For the function y = 2x + 3, the gradient function is f(x) = 2.
4. What is the gradient function of a vertical line?
The gradient function of a vertical line does not exist because the gradient of a vertical line in undefined.
It is not possible to differentiate an equation of the form x = c.