find the maximum and minimum value of function using first and second driver ties test f(x)=x+√(1-x).

your school subject is : math

not: Abubakar tafawa balewa university bauchi ATBU

y = x + (1-x)^(1/2)
y' = 1 + (1/2)(1-x)^(-1/2)(-1)
= 1 - (1/2)(1-x)^(-1/2)

= 0 for a max/min
1 = (1/2) (1/√(1-x)
√(1-x) = 1/2
1-x = 1/4
4-4x=1
x = 3/4
f(3/4) = 3/4 + √(1-3/4)

= 3/4 + 1/2 = 5/4 ----> max

y'' = 0 + (1/4)(1-x)^(-3/2)(-1)
= -(1/4)(1/(1-x)^(3/2) ) )
at x = 3/4
y'' = -(1/4)(1/√1/4)) = negative

so 5/4 is a maximum when x = 3/4