The minimum value of the function f(x)=x32+x-32-4x+1x for  all permissible real x, is

f(x)=x3/2+x−3/2−4x+1xf(x)=x+1x3−3x+1x−4x+1x2−2f(x)=x+1x3−3x+1x−4x+1x2−2 Let g(t)=t3−3t−4t2+8⇒g(t)=t3−4t2−3t+8⇒g'(t)=3t2−8t−3=(t−3)(3t+1)g''(t)=6t−8g''(3)=10>0⇒g(3) is minimum g(3)=27-9-36+8=-10