Find a and b given that the function y=ax√+bx√ has a minimum value of 54 at x = 81.

a.)a=486 and b=6
b.)a=243 and b=6
c.)a=486 and b=3
d.)a=243 and b=9
e.)a=243 and b=3

The value of  A and B given that the function has a minimum value of 54 at x = 81 is 243 and 3 respectively

Given the function

If y= 54 where x = 81, hence

At the minimum point

Differentiate the given function:

Substitute x = 81 to hav:

Substitute equation 2 into 1:

Get the value of A:

Hence the value of  A and B given that the function has a minimum value of 54 at x = 81 is 243 and 3 respectively

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Option e.

Step-by-step explanation:

Consider the given equation is  

The minimum value of function is 54 at x=81.

Substitute y=54 and x=81 in the given function.

Multiply both sides by 9.

             .... (1)

Differentiate the given function with respect to x.

Equate y'=0 t find the critical fpoint.

Substitute x=81 in the above equation.

           .... (2)

Substitute this value in equation (1).

Substitute this value in equation (2).

The value of A is 243 and the value of B is 3. Therefore, the correct option is e.