Find the antiderivative, F(x), with F′(x) = f(x) and F(0) = 1.

Question

f(x) = −7 x

Answer 1

if F' (x) = -7x
then F(x) = -(7/2)x^2 + c
but F(0) = 1
1 = 0(-7/2) + c
c = 1

F(x) = (-7/2)x^2 + 1