Question

Given that the graph of f passes through the point (1, -4) and that the slope of its tangent line at (x,f(x)) is 2x+1, find f(-1) (graph is hypothetical).

Answer 1

well, dy/dx = 2x+1
so y = x^2 + x + c
but (1,-4) lies on it, so
-4 = 1 + 1 + c
c = -6
f(x) = x^2 + x - 6

find f(-1) = ....

Answer 2

I had gotten -6 as an answer earlier but 2nd guessed it, thanks.