What are the critical points of f(x) = e^(x^(1/3))*sqrt(x+8)?

1 Answer
Ahmed A.
Apr 8, 2018

f(x)^/=(3)(1)+(2)(4)

please see below !

Explanation:

f(x)=e^(x^(1/3))*sqrt(x+8)

y=sqrt(x+8) (1)

z=e^(x^(1/3)) (2)

f(x)=z*y

f(x)^/=z^/*y+z*y^/

z=e^(x^(1/3))

x^(1/3)=n

z=e^n

x^(1/3)=n

(dn)/dx=1/3x^(-2/3)

z=e^n

dz/(dn)=e^n

(dz)/(dn) * (dn)/dx = (dz)/dx

(dz)/dx= 1/3x^(-2/3)*e^(x^(1/3)) (3)

y=sqrt(x+8)

u=x+8

(du)/(dx)=1

y=sqrt(u)

dy/(du)=1/2u^(-1/2)

dy/(du)*(du)/(dx)=dy/dx

dy/dx=1/2(x+8)^(-1/2) (4)

f(x)^/=z^/*y+z*y^/

f(x)^/=(3)(1)+(2)(4)

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