Given a polynomial function: f(x)=x4-4x3-8x264a) Find the critical numbers using the derivative.f'(x)=22(x4-4x3-8x264)f'(x)=4y3-12y2-16x=04x(x2-3x-4)=04x=07x=0(x-4)(x1)=0x-4=0=4b) Make a sign diagram for the derivative with all relative extreme points.(-8,-1),(-1,0),(0,4),(4,)c) Write the open intervals where the function is increasing:d) Write the open interval where the function is decreasing: Find the asymptotes of a rational function, f(x)=x-2x3-4x.[Give the asymptotHi please help im new to calculus and im trying to understand how to solve these and how to do it with labeling the derivitives in the correct notation. thank youGiven a polynomial function: f(x)=x4-4x3-8x264a) Find the critical numbers using the derivative.f'(x)=22(x4-4x3-8x264)f'(x)=4y3-12y2-16x=04x(x2-3x-4)=04x=07x=0(x-4)(x1)=0x-4=0=4b) Make a sign diagram for the derivative with all relative extreme points.(-8,-1),(-1,0),(0,4),(4,)c) Write the open intervals where the function is increasing:d) Write the open interval where the function is decreasing: Find the asymptotes of a rational function, f(x)=x-2x3-4x.[Give the asymptotHi please help im new to calculus and im trying to understand how to solve these and how to do it with labeling the derivitives in the correct notation. thank you