Question

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.

1a. f(x) = 48x − 4x²

1b. g(x) = x⁴ − 2x² + 2

1c.y =

x

x2 + 49

1d. f(x) = 9 − 9x, Find the open intervals on which the function is increasing or decreasing. Use a graphing utility to verify your results. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

1e. f(x) = −4x² + 16x Find the critical numbers. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Find the open intervals on which the function is increasing or decreasing. Use a graphing utility to verify your results. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

Answer 1

- (1) (a) f() 48x -4. Critical points are those points where curre Changes, ito slope. sign of df 48-8X. for critical point df 20 48 - X = 0 =6 11 3 (M) = 것 - 212 +2 - 43 - 4 dg da dg 뿄 413 - 44 = 0 20 नर 1+1) C M

- 1. x = 0, 1, and 1 +49 1.C y = dy 24 an do 20 dx for critical points. 226 no 1.d. ton) = 9 -971. dt -9 < 0 ar so tr, < 0 df fire) always decreases. dr in (-os) th) is. neasing. function increasing DNE If we see the graph. then it is always. decreasing (0,9) (1,0) 7 x y = 9-gn.