Find a particular solution of the differential equation f'(x)=-2x whose graph passes through the point(-1, 1)

Question

i dont understand

Answer 1

What you have to do is integrate -2x with respect to dx, and find the 'c'

f(x) = integral (-2x)dx = -2(x^2)/2 + c = -x^2 + c

Now, let's find c such that f(-1) = 1

1 = -(-1)^2 + c = -1 + c // add 1

c = 2

f(x) = -x^2 + 2