Question

Find f(x) if f′(x)=(−3)⋅x+(−1) and f(−4)=−1.

I know if you find the antiderivative of f'(x) it is -3x^2/2 - x + c but what do I do next to find the function f(x)?

Answer 1

You wan to find c, so plug in the point (-4,-1) which is on this particular solution curve:

(-3*16)/(2+4+c) = -1

The way the function is worded makes me suspect a typo. Fix that, and find c for a particular solution.