Question

Let f(x)= ln(4x)/x , for 0 < x ≤ 5. Points P(0.25 , 0) and Q are on the curve of f . The tangent to the curve of f at P is perpendicular to the tangent at Q. Find the coordinates of Q

Answer 1

so, we have
y = ln(4x)/x
y' = (1-ln(4x))/x^2
so at P, y' = 4
That means y' at Q is -1/4
so now we need
(1 - ln(4x))/x^2 = -1/4
x = 0.79 or 2.14
You can find f(x) there

Answer 2

Q = (5, ln(20)).