Using the graphing strategy discussed in class, sketch a graph of the function m) = $0: 419'\" + 30: 4)\". Label any intercepts. relative extrema. points of inection. holes. and asymptotes. Identify the intervals where f is increasing. decreasing. concave up, and concave down. Show your steps for finding and simplifying ['[IJ and f\"(;r). Curve sketching steps 1. Identify the domain, asymptotes, and intercepts of f. Also consider lim f(x) and lim f(x). 2. Find the C.N. and P.P.O.I. of f. critical numbers " possible points of inflation 3. Divide the number line using the points from and 2. For each interval created, determine whether f is *increasing, decreasing, concave up, or concave down. Also, evaluate f at each of these points. 4. Sketch the graph.1. Use calculus to graph y = 25 - 5.3. =f (x) Solution ! a. Don: IR asymptotes : none 25 - 5x3 =0 *' (x 2 -5)=0 = x:0, +15 lim f GC) = 00 lim f ( x) = -00 76-7-00 b . f' ( x ) = 574 - 15x2 = 5x2 ( x 2- 3) =0 x:0 x-+53 C.p. : - 53' , 0, $3' f" (x ) = 20x3 -30x 10x ( 2 x 2 - 3 ) =0 x=0, x#12 =$10 bles P. P.O. I :. 2C. f ( x ) I f" ( x ) If" ( x ) 1 Conclusion (-00, - $3).2 increasing, concave down X = -53' O -3053 local maximum decreasing concave down 6.4 O PO I (-56/2, 021 + decreasing concare up x = 0 O O POT decreasing concave down x = JOK -6. 4 O POT + decreasing concure up 21 =13 -653 O local minimum (53 00 + + increasing on came up