Answer the following questions related to the derivative and the tangent to a curve.
a. (i) Define the derivative of a function f at a point a by using the limit of the difference quotient.
b. (ii) Describe the geometrical meaning of the derivative at a point on the graph of f.
c. (iii) Explain why the existence of a finite derivative at a point guarantees a unique tangent line there.
d. (iv) State the point–slope form of the equation of a straight line with slope m passing through the point (x0,y0).