For the function f(x) =xe^-(x^2 -x)/2
1) Determine the linearization L(x) of f(x) at x=1.
2) Use the linearization of f(x) at x=1 to estimate the value of f(1.2).
The linearization is just the tangent line at x=1.
Assuming your parentheses are correct, and the 1/2 is not part of the exponent, then
y' = 1/2 e^(x-x^2) (-2x^2+x+1)
y'(1) = 1/2 * e^0 (-2+1+1) = 0
So the linearization is just the line y = 1/2