Question

Find the maximum and minimum values of 4x 9 12 1​

Answer 1

Answer:

Let f(x) = 4x+9y……..(1)

Since xy = 4, we have y=4/x. Substituting in (1) we get f(x) = 4x+(36/x) …….(2)

Differentiating we get f ' (x) = 4 - (36/x^2)…..(2)

For maxima or minima, f ‘ (x) = 0

=> 4 - (36/x^2) =0 => (4x^2 - 36)/x^2 = 0 which gives x= +/- 3

Differentiating (2), f ‘’ (x) = 72/x^3

When x= +3 , f ‘’ (x) is clearly +ve. Therefore f(x) at (2) gives minima and the minimum value is 24.

When x= -3, f ‘’ (x) is -ve. Therefore, f(x) has maxima at x= -3. The maximum value is -24.