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Functions f, g - [Iran Second Round 1986]

Source:

December 24, 2010
functioncalculusderivativelimitalgebra proposedalgebra

Problem Statement

(a) Sketch the diagram of the function ff if f(x)=4x(1-|x|) ,   |x| \leq 1.
(b) Does there exist derivative of ff in the point x=0 ?x=0 \ ?
(c) Let gg be a function such that g(x)={f(x)xemsp;:x≠0 4    emsp;:x=0g(x)=\left\{\begin{array}{cc}\frac{f(x)}{x}   : x \neq 0\\ \text{ } \\ 4 \ \ \ \   : x=0\end{array}\right. Is the function gg continuous in the point x=0 ?x=0 \ ?
(d) Sketch the diagram of g.g.
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