Question

2. Let f(x) = x* – 18x²+4. a) Find the intervals on which f is increasing or decreasing. b) Find the local maximum and minimum values off. c) Find the intervals of concavity and the inflection points. d) Use the information from a-c to make a rough sketch of the graph.
show work

Answer 1

Ginen function tex)= x4–183274 را function will be increasing, when t'exy so, and function will be decreasing, when flex <o. t(a)= 423_360 = 48(2²9) f'(x) = 4x(x-3)(x+3) Now + + -3 o 3 t'has so it teasco it XE (-3,o] U (3, w) x 61-603-3) 0(0,3) Increasing when Decreasing when (-3,0] U (3,co) x6 (-6,-3] U20,3] (أنا To find local maxima and minima - "X)= 1222-36 (local maxima.) at x=0 at a=-3, t'(-3) = 672 so (locul minima) at a=3 t(3) = (local minimal tica)=-36co >= 7230 local maxime wilue ofco)=4 local and +63)=-77 minima walne (1-3)

liii) Concquity - th(a) = 12203_36 12(X-13)(2+33) Concque up when a scu3 or 27 13 Bcas 23 concque down when Point of inflaction! 1222-36=0 13, -83 X uw 1 Y=40 4 0.4744 x 0 -0.4744