calculus
posted by Tina .
Find constants a and b in the function f(x)=ax^b/(ln(x)) such that f(19)=1 and the function has a local minimum at x=19. What is a and b?

calculus 
Steve
Just plug and chug:
f = ax^b/lnx
1 = a*19^b / ln 19
a * 19^b = 2.944
f' = (abx^(b1) * lnx)  ax^(b1))/ln^2(x)
= [ax^(b1) * (b*ln x1)]/ln^2(x)
to get f'=0, we need b*lnx = 1
b*ln19 = 1
b = 1/ln19
a* 19^b = 2.944
a*19^(1/ln19) = a * 19^.3396 = a*2.718 = 2.944
a = 1.083
So, if my math is right, f(x) = 1.083*x^.3396/lnx
Respond to this Question
Similar Questions

calculus
A cubic polynomial function f is defined by f(x)= 4x^3+ab^2+bx+k where a, b, k, are constants. The function f has a local minimum at x=2 A. Fine the vales of a and b B. If you integrate f(x) dx =32 from o to 1, what is the value of … 
Calculus  Functions?
#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = 1, and the graph of f has a point of inflection at x= 2 a.) Find the values of a … 
Calculus
Find constants a and b in the equation f(x)= ax^b/(ln(x)) such that f(1/8)= 1 and the function has a local minimum at x= 1/8 
Calculus (pleas help!)
Find constants a and b in the function f(x)=axe^bx such that f(1/8)=1 and the function has a local maximum at x=1/8. a= b= Please help me with this one... 
Calculus 1
Find constants a and b in the equation f(x)= ax^b/(ln(x)) such that f(1/3)= 1 and the function has a local minimum at x= 1/3 
Calculus
Find constants a and b in the function f(x)=axe^(bX) such that f(1/8)=1 and the function has a local maximum at x=1/8. 
Calculus
Find constants a and b in the function f(x)=axe^(bx)such that f(1/7)=1 and the function has a local maximum at x=1/7. a = b = 
Calculus
Find constants a and b in the function f(x)=axbln(x) such that f(15)=1 and the function has a local minimum at x=15. 
Calculus
Find constants a and b in the function f(x)=(ax^b)ln(x) such that f(1/5)=1 and the function has a local minimum at x=1/5. 
Calculus
Find constants a and b in the function ax^b/ln(x) such that f(1/5)=1 and there is a local min at x=1/5