Let f and g be differentiable and continuous functions for all real numbers such that f(x) = 3:3 +91:2 +2 ,and 1 90:) = ()x'* + 2x3 + 1. Find the...

1.    Find the location of all local extrema, i.e. local maximum and local minimum for the functions  and  using

a)   the First derivative test

b)   the Second derivative test

Note: need to show work completely and explain your work including the solutions as well.

Let f and g be differentiable and continuous functions for all real numbers such thatf(x) = 3::3 +91:2 +2,and 190:) = (§)x‘* + 2x3 + 1. 1. Find the location of all local extrema, i.e. local maximum and local minimum for thefunctions f and 9 using a) the First derivative testb) the Second derivative test