anyone ready to solve this challenging question?

Question

given that f(x) = 4 / square root of (x^2 + 9)

and the equation of the normal at the point of inflexion lying in the 1st quadrant is m*(square of n)*y - k*(square root of l)*x + 665 = 0
find the values of k, l , m , n

ps: i found f'' (x) to be : 4*(square root of (x^2 + 9)) * (2x^2-9) / (x^2 + 9 ) ^3

Answer 1

f ''(x) is good !
the point of inflexion is (in the 1st quadrant) for x = a = 3*sqrt(2)/2

f '(a) = .... = - 8 / [27*sqrt(3)]

f(a) = ... = 4*sqrt(6) / 9

the normal is perpendicular to the tangent, then the equation of the normal is :

y = 27*sqrt(3)/8 [x - a] + f(a)
= ...

I find m = 144
n = 6
k = 1458
l = 2

No ?

Answer 2

Impossible to solve uniquely. I didn't bother to solve for the equation of the normal given f(x) so I don't know that it *has* a point of inflexion in the first quadrant but the following are simply constants with respect to any (possibly existent) normal line:

m*sqrt(n)
k*sqrt(l)

Since this is the case, it is not possible to solve for unique parameters (i.e., any solution set would have m = f(n), k = g(l).

Answer 3

um, false?