8. For each case, find the points of inflection. a) /(x)=x-x b) /(x) = x+ 1 c) /(x) = (x+1)$13 d) f(x) =(1-x) (1+x)] e) /(x)=x Inx f) f(x) =x-sinx 9. Find c given that the graph of /(x) = ex- +1/x- has a point of inflection at (1, f (1) . 10. Use the second derivative test to find the local maximum and minimum values of each function. a) f(x)=x -6x2 b) f(x)=x4 - 6x] -5 c) f(x) =- X d) /(x) =. X x3 + 1 (x- 1)] 11. Find the local minimum and maximum values for. a) y=x bj y=x* 6. Second Derivative compute /"(x) find points where "(x) = 0or /"(x) DNE find points of inflection find intervals of concavity upward/downward check the local extrema using the second derivative test 7. Sketching use broken lines to draw the asymptotes plot x- and y- intercepts, extrema, and inflection points draw the curve near the asymptotes sketch the curve 12. Sketch the graph of the following polynomial functions. a) f(x) = 2x - 3x- -36x b) f(x) = 3x) - 5x] c) f(x)= (x-1)] d) f(x) = x (x+3) e) f(x) = (x - 3)(x] -5) 13. Sketch the graph of the following rational functions. a) /(x) = x+1 b) f(x) =- x3 - 1 c) f(x) =. +1 d) f (x) = x3+ 1 14. A rectangle has a perimeter of 100m . What length and width should it have so that its area is a maximum. What is the maximum value of its area? 15. If 2700cm of material is available to make a box with a square base and open top, find the dimensions of the box that give the largest volume of the box. What is the maximum value of the volume? 16. A rectangular piece of paper with perimeter 100cm is to be rolled to form a cylindrical tube. Find the dimensions of the paper that will produce a tube with maximum volume. 17. A farmer wants to fence an area of 240,000m in a rectangular field and divide it in half with a fence parallel to one of the sides of the rectangle. How can be done so as to minimize the cost of the fence? 18. A metal cylinder container with an open top is to hold If . If there is no waste in construction, find the dimensions that require the least amount of material