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Old December 1st, 2008, 06:57 AM
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Quote:
Originally Posted by helppalusmath View Post
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 f'(x) = -13 tan^{-1} (x) + C. Do you see why?

2. \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.
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