Four analytic functions are defined for all real x.
u(x)=3x2−3v(x)=2sinxw(x)=x3−3x+1z(x)=6x
Exactly three of these functions constitute the graphs of a differentiable function f together with its first and second derivatives. The remaining function does not belong to that set.
a. Part 1: Identify which functions represent f, f′ and f′′, and indicate which function is extraneous. Provide complete justification, including at least one derivative computation or comparison for each assignment.
b. Part 2: For the function you have designated as f, determine all intervals of concavity and locate every point of inflection.
c. Part 3: Explain why the function you declared extraneous cannot represent any of f, f′ or f′′, even up to multiplication by a non-zero constant factor.