What is the equation of the function f whose graph passes through the given point?

Question

Find the equation of the function f whose graph passes through the given point. (Remember to use absolute values where appropriate.)

f ' (x) = x^3 - 4x^2 + 3 / x - 3

point: (4,-9)

f(x) = _____

Answer 1

You would need to perform two steps.

First, take the antiderivaitve of the expression labled f' (x). The result will end in a constant: + C.

Then substitute 4 for x in your answer, and equal the entire thing to -9.

Solve for C.

Rewrite your antiderivative with the number you got in place of C.

That's it.

Hint: Remember, the antiderivative of 1/x in ln|x|.