Question

Find the intervals on which f(x) is increasing and the intervals on which f(x) is decreasing. Then sketch the graph. Add horizontal tangent lines. f(x)=4x4 -32x2 Compute the derivative of f(x). f'(x)= Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function is increasing on (Type your answer using interval notation. Use a comma to separate answers as needed.) OB. The function is never increasing Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function is decreasing on (Type your answer using interval notation. Use a comma to separate answers as needed.) OB. There function is never decreasing Choose the correct graph of f(x) = 4x4 - 32x2 with the correct horizontal tangent line below. Click to select your answer(s).

Answer 1

11 +(3P+32°+92 +27 -672-102) - 2 ( x 3 - 3x² - gx +27) T7 fow= -x3 + x² tx-3 f(x) = 4X² - 32x2 differenciate both side with respect tox. f'(W = 16x- 32822 = 16x² - 640 f'(w=0 1623-642 for end point, X3 2-0 x = -2 16x( X²4)=0 axtg) (x-2)=0 g 21270 then a=2 so, end point =-20, 2 Now, find f (x), differenciale equation © with scopfact to y f" (x) = 48 x 64 f"(x) = 48X1-2,²-64 - 192-64 = 128

put ato flow= f" = 0 -64 = -64 but x=2, f(x)= 48 x 2 = 64 = 192-64 2 = 128 f'(x) (170 for x= -2,2 local At meant function has a minimum at value at these point floweo for x=0 It means at this point function have maximum value.

80, increasing interval (- 0,- 2) & (012) Decreasing interval, 620141260) interval (-2,0) 8 (200) Decreasing interval (-00,-2) & (012) 80, increasing

at x=2, fow= 4(2) 4-gg (2)" = 64 - 128 =-64 4 at x=-2, f(x) = 4(-2) - 32(2) ? -64 at x=0 foni= 409 32 (0)? fox- to Now, plat graph as ao al 2-0 y 3 2 + 282 -252 O 3 1 3 1-64 fea 2- intercept, bet fixo, 4X4_322²0 4x2(x²-8)=0 42-(2 +212) (7-252) 20 x=0, x=-252, +252