Let, the numbers are: x, (24-x) Let, P(x) denote their products. Then, we have: P(x) = x(24-x) = 24x - x² P'(x) = 24-2x P''(x) = -2
Now, P'(x) = 0 ⇒ x = 12 Also, P''(12) = -2 < 0
So, By second derivative test, x = 12 is the point of local maxima of p. Hence the product of the numbers is the maximum when the numbers are 12 and (24-12) = 12
If a number can be written or can be converted to p/q form, where p and q are integers and q is a non-zero number, then it is said to be rational and if it cannot be written in this form, then it is irrational.
