y'=2x-7

Let y'=0 x=7/2.

When x changes, y' y changes as follows (list)

x (-∞，7/2) 7/2 (7/2，+∞)

y' - 0 +

Y minimum decrease -25/4 increase.

(2) Solution: y = 3x 4+4x 3

y'= 12x^3+ 12x^2= 12x^2(x+ 1)

Let y'=0 x 1=- 1 x2=0.

When x changes, y' y changes as follows (list)

x (-∞，- 1) - 1 (- 1，0) 0 (0，+∞)

y' - 0 + 0 +

Y decreasing minimum-1 increasing.

(3) solution: y = x 3-x 2-4x+4.

y'=3x^2-2x-4

Is it wrong to make y'=0 x without understanding?

(4) solution: y = 2x 2-x 4

y'=4x-4x^3=4x( 1-x)( 1+x)

Let y' = 0x1=-1x 2 = 0x3 =1.

When x changes, y' y changes as follows (list)

x (-∞，- 1) - 1 (- 1，0) 0 (0， 1) 1 ( 1，+∞)

y' + 0 - 0 + 0 -

Y increasing maximum 1 decreasing minimum 0 increasing maximum 1 decreasing.

(5) solution: y =-x 3+3x-5

y'=-3x^2+3=3( 1+x)( 1-x)

Let y' = 0x1=-1x 2 =1.

When x changes, y' y changes as follows (list)

x (-∞，- 1) - 1 (- 1， 1) 1 ( 1，+∞)

y' - 0 + 0 -

Y decreases by a minimum of -7 and increases by a maximum of -3.

(6) Solution: y = 4x 3-3x 2-6x+2

y'= 12x^2-6x-6=6(2x+ 1)(x- 1)

Let y' = 0x1=-1/2x2 =1.

When x changes, y' y changes as follows (list)

x (-∞，- 1/2)- 1/2(- 1/2， 1) 1 ( 1，+∞)

y' + 0 - 0 +

Y increases the maximum value 15/4 decreases the minimum value -3 increases.