Question

4. Two positive numbers are such that one is twice the other. The product of these two number is 1-17/32​

Answer 1

We have to maxims x

2

y

5

and we have x+y=35

So put x=35−y in x

2

y

5

we get (1225+y

2

−70y)(y

5

)

f(y)=1225y

5

+y

7

−70y

6

f

′

(y)=6125y

4

+7y

6

−420y

5

Putting this to zero we get

y=35,y=25

f

′′

(y)=24500y

3

+42y

5

−2100y

4

f

′′

(35)=24500×35

3

+42×35

5

−2100×35

4

f

′′

(35)>0

At y=25

f

′′

(25)=24500×25

3

+42×25

5

−2100×25

4

f

′′

(25)<0

So given function will have maxima when y=25

So x=10

Answer verified