Question

the sum of two number is 24.the greatest product of these two numbers can be

Answer 1

144 which is equal to 12×12

Answer 2

Step 1:

Given

Sum of two no = 24

Product = largest

Let the required number be x and (24−x)

Their product (P)=x(24−x)

=24x−x2

Step 2:

For maximum value

Now dPdx=0

P=24x−x2

Differentiating with respect to x we get

dPdx=24−2x

24−2x=0

−2x=−24

x=12

d2Pdx2=−2<0

⇒P is minimum at x=12

Hence the required numbers are 12 and (24−12)

⇒12