# More antiderivative questions

• Nov 30th 2008, 06:33 PM
helppalusmath
More antiderivative questions
1) f(x) = -13/(1 +x^2 )

The question is to find the antiderivative. I'd assume it would be inverse tangent X -13. Am I correct?

2) (1 pt) Given that the graph of f(x) passes through the point (5,5) and that the slope of its tangent line at (x,f(x)) is 4x +5 what is f(3)?
• Dec 1st 2008, 04:57 AM
mr fantastic
Quote:

Originally Posted by helppalusmath
1) f(x) = -13/(1 +x^2 )

The question is to find the antiderivative. I'd assume it would be inverse tangent X -13. Am I correct?

2) (1 pt) Given that the graph of f(x) passes through the point (5,5) and that the slope of its tangent line at (x,f(x)) is 4x +5 what is f(3)?

1. No. Try $\displaystyle f'(x) = -13 tan^{-1} (x) + C$. Do you see why?

2. $\displaystyle \frac{dy}{dx} = 4x + 5 \Rightarrow y = 2x^2 + 5x + C$. Substitute (5, 5) to get the value of C. Then substitute x = 3 to get the required value of y.
• Dec 1st 2008, 05:02 AM
Chop Suey
Quote:

Originally Posted by mr fantastic
1. No. Try $\displaystyle f'(x) = -13 tan^{-1} (x) + C$. Do you see why?

I think he meant "inverse tangent times -13"
• Dec 1st 2008, 05:42 AM
mr fantastic
Quote:

Originally Posted by Chop Suey
I think he meant "inverse tangent times -13"

Hmmmph .... That's what I tell my bank teller every time I bank a cheque for say $30.50 ..... "I think she meant$3050", I say ..... It doesn't work with bank tellers and it doesn't work examiners .... Examiners don't play guessing games, careless mistakes can be costly.