Bài tập Toán DIFFERENTIATION 10

Question 1 non calculator For each of the following cubic equations find the coordinates of their stationary points and determine their nature... Question 2 For each of the following equ

STATIONARY POINTS

Question 1 (non calculator)

For each of the following cubic equations find the coordinates of their stationary points and determine their nature

a) y=x3−3x2−9x+3

b) y=x3+12x2+45x+50

c) y=2x3−6x2+12

d) y=25 24− x+9x2−x3

min 3, 24 , max− −1,8 , min(− −3, 4 , max) (−5, 0) min 2, 4 , max 0,12 , ( ) ( )

min 2,5 , max 4,9

Question 2

For each of the following equations find the coordinates of their stationary points and determine their nature

x

x

c) y= −x 4 x, x> 0

d) y 4x2 1, x 0

x

min 2, 4 , max − −2, 4 , min 2,12 , ( ) min 4, 4( − ) , min( )1,3

2