Question

i just learned this today. and i am having a hard time grasping the information.

2. Sketch a possible graph of y = f(x), using the given information about the first and second derivatives. Assume that the function is defined and continuous for all real values of x. [7 pts] y = 0 y'>0! y = 0 Ly<0 y'> т 01 12 13 -- y = 0 y = 0 /' <0},">0} y <0 C

Answer 1

Sketch a possible graph of y = f(x) using the ginen information (1) y'=0 at x, and az Therefore x, and az are critical points and may have extreme point Now y" atac=0 so ac, is not a extreme point y" at az y"<0 hence Xz is local maximum. So only one extrema that is az is local maximum. (2) y'>0 (-00, 061) U (X, 103) Therefore graph is increasing (100, 43) y' Lo (263,00) So graphis decreasing on (263,00) (3) y"=0 at x, and X2 hence xi and Ka are inflection points (4) y"<0 on (-60,51) So graphis concare down on (-0, x) Y" so on (X1,83) So graphic concave ulo on (X, 1862) yo co on (x2.00) so gralph is concave down on (X2,00) Now possible graph on graph shoot.