For the function K(x)=3xe4x, do the following:(a) Determine its critical number(s) if exists. (Use fractions for constants.)Answer: xc=(b) Use the First-Derivative Test to classify each as a relative maximum or minimum, or neither:Near the critical number xc=, when xxcxc=x, the first derivative is- select-0, and when xxc, the first derivative is-9 elod , Therefore the function has --Selectat xc=This is similar to Section 3.4 Problem 26 :For the function s(x)=5x3-x4, do the following:(a) Determine is critical number(s) if exists. List from least value.Answer: xCl=xc2=(b) Use the First-Derivative Test to classify each as a relative maximum or minimum, or neither:Whear the criticat number xct=, when x2xc1, the firt dertiative is - Seloct -, and when x0xct, the firt derivative is . Therefore the function has -Select at xC1''Near the critical number xC2w, when x>xazxca=x, the first derivative is- Select -9, and when x>xaz, the firgt derivative is, Therefore the function has --5nlociat xca= Hint: Follow Example 4.For the function s[x)=5x3-x4, do the following;(a) Determine its critical number(s) if exists. List from least value.Retrwer:-xc1=?c,2F1.(b) Use the First-Derivative Test to classiry each as a relative maximum or minimum, or nether:Near the critical number xc1=1, when =hat(**)c1xC2=-hat(f)x>xczxc2=x, the first derivative is- Select -hat(f), and when x>xcz, the first derivative is. Therefore the function has -selectat xc2= Hint: Follow Example 4.x, the first derivative is- Select =(