Question

3.) Sketch the curve y = x - 3x1/. Before sketching please find intercepts, intervals of increasing and decreasing intervals of concavity, local extreme values, and points of inflection. (5 points)

Answer 1

all real numbers Domain: y = ne-3x is defined for so its domain is Ron (-Do) Imtercepta: y-intercept as a Fore re-intercept, put y = 0 and solve for ne 2-3x = 0 which gives no andre = 135 so a intercepts are o and t8u3 ((e) = re-3n ول flume) = - +3 re's = -(x-3m's) = -f(x) So, this function is an ond function and symmetrin about the origine Living (ne - Sne's )= 1 So there is no horizombl asymptote and this function >100 very cohet 80 thee ei mo verlica au es clefined 13 = 1 - 212 = 0 or y =0 when on x²=1 are = t / And g'ie mot defined at ne=0 So, the critical numbers are -1,0, and So we divide the interval (.oo, as into the intervals C-x-1), (-1,0), (0, 1) and (10) and we have wito when - linero and opne1, soy is deereanime om (-1,0)(0,1) y yo cohemales-1 and Karoo so y is increasing om (-0, -1) and (10)

is a y has local maximum at n = -1 G has local minimum at a=1 ximum minimum at x = -1 and that at a=1 that is 2 - y = 1-ne 213 into soy is concare downw So, y "To cohem an (-0,0) so y is concave upwared on So y ">o whom oine roo €0,00) point (0,0) Thus y has an inflection H