AP Calculus BC help? Find the point on the graph of y=1/(1+X^2) where the tangent line has the greatest slope, and the point where the tangent line has the least slope.
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nickname09
ANSWERS: 3
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Also, I am only 16 years old and just want some direction on how to start the problem, not the answer. I would appreciate if you would not call me "stupid" etc., I got plenty of that from the msn qna site.
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First, start working on what they asked you. The tangent of the equation, or the derivative. then, get a graphing calculator and graph the original equation and its derivative. you should see the highest point of the original equation is also when the derivative equals to zero. With this, the highest and lowest points of a equation is when the derivative of the equation is zero. You will use this idea to solve. Look up maximum/minimum in Calc for further explanation. The question asked for the greatest slope and lowest slope of the original equation. So, find the second derivative, derivative of the derivative, and set it to zero, and solve. The answer will give you the x-value of the highest/lowest slope. Plug it in to the equation to get its y-value and then you'll have the points. To graphs to be sure of your answer if you get stuck.
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Even though this is clearly not homework, it is still to your benefit to do it yourself. So I won't do the algebra for you, just point out what to look for. Can you differentiate this function? What does the derivative tell you about a function? The derivative tells you the slope of the tangent line. So asking what the point of maximum slope is, means you want to find the point where the derivative is maximized. You can find that point by inspection of the derivative function, or for more difficult problems, by setting the derivative of the derivative to zero. Note, the derivative of the derivative is the second derivative of your function. Solve for the point(s) where this happens. While a graphing calculator can be useful here, pencil and paper is a very good way to learn. Use the calculator to verify your conclusions and to give you intuition to the solution. Finally, I'll note that the question as written seems slightly ambiguous to me. Is the request for the point of least slope that point where the slope is zero? Or does this ask for the point of most negative slope?
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