Question

Find
f(x) if f(2) = 2
and the tangent line at x has slope
(x − 1)e^(x^2 − 2x)

Answer 1

If f(x) is the function, then f'(x) is the slope of the tangent line at x.
They have given you f'(x) = (x − 1)e^(x^2 − 2x) and are asking for f(x).
Integrate and you will have f(x).
The integration will introduce a constant which can be resolved by setting x = 2 and f(x) as 2 because they give you f(2) = 2.

Answer 2

so what would i do?