Mathematical problems. Find the function y= root number (x+27)+ root number (13-x)+ root number X.

Then use derivative test, the simplest method:

The known function y = √ (x+27)+√ (13-x)+√ x.

Derivative y' =1/(2 √ x)+1/[2 √ (x+27)]-1/[2 √ (13-x))]

Let y'=0

1/(2√x)+ 1/[2 √( x+27)]- 1/[2 √( 13-x))]= 0

The unique maximum value of the solution x=9.

Continue the second derivative y'' =-1[4x (3/2)]-1[4 (x+27) (3/2)]-1[4 (13-x)].

Substituting x value into y'' test:

y ' '(9)=- 1/ 108- 1/864- 1/32

=- 1/24 & lt； According to the definition of the second derivative, 0 is the maximum value when x=9.

The maximum value y(9)=√(9+27)+√( 13-9)+√9.

=√36+√4+√9

=6+2+3

= 1 1

∴ The maximum value at point (9, 1 1) is1,and there is no minimum value.

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