Example (a) You are given the following information about a function f(x) :f(x)=-3x515x4-5x3-45x2-20f'(x)=-15x(x-2)(x-3)(x1)f''(x)=30(1-x)(2x2-4x-3)Describe all intervals on which f(x) is increasing or decreasing. Identify any maxima or minima (x-coordinates only), and indicate whether they are local or global extrema. Be sure to support your answers.(b) You are given the following function g(x) :g(x)=3x4-4x3Describe all intervals on which g(x) is concave up or concave down. Identify any inflection points (x-coordinates only). Be sure to support your answers.(c) Draw a graph of a function h(x) that passes through the points (1,3) and (3,0) and meets the following requirements. Note that there are many possible graphs that would meet these conditions; you are only being asked to sketch one such graph. Be sure to label maxima, minima, point(s) of inflection, and any other features of interest on your graph.h(1) is a global maximum valueh'(x)>0 over (-,1)(3,);,h'(x)<0 over (1,3);,h'(1)=0=h'(3)h''(x)>0 over (2,4);,h''(x)<0 over (-,2)(4,);,h''(2)=0=h''(4)