Answer the following questions concerning the notion of derivative.
a. (i) State the definition of the derivative of a real-valued function f at the point x=a.
b. (ii) Describe geometrically why the derivative of f at a is interpreted as the slope of the tangent to the graph of y=f(x) at the point (a,f(a)).
c. (iii) For the function f(x)=∣x∣, test whether the derivative exists at x=0. Show every step of your working and give a clear reason for your conclusion.