Answer:
1/6
Step-by-step explanation:
Given the function
f(x)=x^3+x^2+x
Get the inverse. Let y = f(x)
y = x^3+x^2+x
Replace y with x
x = y³+y²+y
Differentiate with respect to x
1 =3y²dy/dx + 2ydy/dx + dy/dx
1 = (3y²+2y+1)dy/dx
dy/dx = 1/3y²+2y+1
g'(x) = 1/3(g(x))²+2g(x)+1
If x = 3
g'(3) = 1/3(g(3))²+2g(3)+1
g'(3) =1/3(1)²+2(1)+1
g'(3) = 1/3+2+1
g'(3) = 1/6
Hence g'(3) = 1/6
