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Series of Various Calculour Questions Attached.
You do not need to show your work for this one because I would simply like to compare your answers with mine so that I am sure that I did everything correct on mine. Please just write your answer after each number. I will know which problems I will have to study in detail with your help. Thank you very much.
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12. f'(x) = 1/(1-x)^2
1. Find all the critical numbers: .
2. Find all the extrema in the interval [0, ] if y = x + sin x.
3. Find the absolute maximum and absolute minimum of f on the interval (-1,2].
4. Consider . Find all values, c, in the interval [0,1] such that the slope of the tangent line to the graph of f at c is parallel to the secant line through the points (0,f(0)) and (1,f(1)).
5. Find all open intervals on which is decreasing.
6. Find the relative extrema of , including the designation of maximum or minimum.
7. A differentiable function f has only one critical number: x = -3. Identify the relative extrema of f at (-3,f(-3)) if f'(-4) = ½ and f'(-2) = -1.
8. Find all the intervals on which the graph of the function is concave upward: .
9. Find all points of inflection:
10. Find all horizontal asymptotes: .
12. Calculate 3 iterations of Newton's Method to approximate the real zero of . Use as the initial guess and round to 4 decimal places after each iteration.
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