Fill in the blanks in each of the following
The least value of the function (a > 0, b > 0, x > 0) is ______.
Given (a > 0, b > 0, x > 0)
Now apply the derivative we get
Now applying the sum rule of differentiation we get
Now applying the quotient rule of differentiation on second part we get
We will equate this with 0 to get critical points,
f’(x)=0
Now second derivative gives,
Now apply the derivative we get
Now applying the sum rule of differentiation we get
Now applying the quotient rule of differentiation on second part we get
We will equate this with we get
Thus the least value of f(x) is
Multiply and divide by , we get
Hence the least value of the function (a > 0, b > 0, x > 0) is