*AP calc problem* a function passes through (1,6). the slope of the tangent line of (x,f(x)) is 2x+1. find f(2)

Question

anonymous · Answer

you find the anti derivative of that slope to get the original function then plug in the point to solve for the constant to get f(x), that way you can find f(2)

anonymous · Answer

+1 for mentioning the constant

anonymous · Answer

i guess I'm more of a visual learner. ik that the anti derivative is $$x^{2}+x$$ what do you do after this? an equation or drawing and ill give you the medal

anonymous · Answer

x^2 + x + C, don't forget the constant as @jayz657  mentioned.  YOu have to include it because the derivative of a constant is zero, so you need to solve for that constant first with your (x,y) coordinate.

anonymous · Answer

c is 4 i take it …
clarification?

anonymous · Answer

sure i can draw something

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like @mathbrz said the anti derivative is x^2 + x + c
since you know that (1,6) is a point on the function then you can plug that in to get the full equation