The known function f (x) = ((x ^ 2) / 2) - alnx (a)

The known function f (x) = ((x ^ 2) / 2) - alnx (a)

y=-cos2x+acosx+5/8a-1/2=y=1-2(cosx)^2+acosx+5/8a-1/2=-2(cosx-a/4)^2+5/8a+1/2+a^2/8

Functions f (x) = x ^ 2-1 and G (x) = alnx a ≠ 0
If the image of F (x), G (x) has a common tangent at the point (1,0), find the real number a

f'(x)=2x
g'(x)=a/x
The image of F (x), G (x) has a common tangent at point (1,0), so when x = 1,
f'(1)=g'(1)=a/1=2
So a = 2

Given the function f (x) = x ^ 2-alnx (a ∈ R), when x = 1, f (x) obtains the extremum, and the value of a is obtained

f(x) =x^2-alnx
f'(x) = 2x - a/x
f'(1) = 2-a =0
a = 2