DE07 DE THI THU THPT LE HONG PHONG HCM 2015 1

35

1

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* y' =

* y' > 0, x D

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y

2

2

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* : (0; 1); ( ; 0); ( 2; 5); ( ; )

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(d) (C) (x0; y0)

(d): y y0= y'(x0)(x x0)

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3 + 2x0 1 = 4x0+ 4 2x0= 8 x0= 4 y0= 3; y'( 4) =

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* I2= :

-5 -4 -3 -2 -1 1 2 3

-2 -1 1 2 3 4 5 6

x y

TRUNG TÂM D Y THÊM LÊ H NG PHONG

1 2sin2x + 3sinx = 2 2sin2x 3sinx + 1 = 0

* sinx = 1

* sinx = sin

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= log3x (x > 0)

(1)

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t 2

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2

, > 0

)

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( ) n 2 + 6 = 15 n = 11.

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2

k = 9

2

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b

8

0.5

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TRUNG TÂM D Y THÊM LÊ H NG PHONG

= (A; B) (A2+ B2> 0) CD: A(x + 3) + B(y + 3) = 0

Ax + By + 3A + 3B = 0

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: SBCD = SACD= 18

25(36A2+ 48AB + 16B2) = 90(A2+ B2)

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* : = 3 A = 1 (CD): x 3y 6 = 0 D(3d + 6; d)

: CD2= 90 (3d + 9)2+ (d + 3)2= 90 (d + 3)2= 9 d = 0 hay d = 6 D(6; 0) ( ) hay D( 12; 6) ( ) (6; 0) A(0; 2)

( ; ) B( 3; 1)

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* : = 27 A = 31 CD: 31x 27y + 12 = 0

B( 3; 1).

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: 2 x 2 0

: (3) 2t = t2

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M

D

A B

C

9 Cho x, 2+ y2 = 2 :

* 4 = (12+ 12)(x2+ y2) (x + y)2 2 x + y

2(x3+ y3) (x + y)(x3+ y3) x3+ y3 2

= x3+ y3 ;

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:

* 23 = (x2 + y2)3= x6+ y6+ 3x2y2(x2+ y2)

= x6+ y6+ 6x2y2= (x3+ y3)2 2x3y3+ 6x2y2

2x 3 y 3 6x 2 y 2 = t 2 8

* 2(x3+ y3) = (x3+ y3)(x2+ y2) = x5+ y5+ x2y3+ x3y2= x5+ y5+ x2y2(x + y)

x 5 + y 5 + x 2 y 2 (x + y) = 2t.

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= 4x3y3+ 12x2y2+ 5(x5+ y5) + 5x2y2

= 2(2x3y3 6x2y2)+ 5(x5+ y5) + 5x2y2

= 2(t2 8) + 5[x5+ y5+ x2y2(x + y)] = 2t2+ 10t + 16 = f(t)

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f '(t) = 4t + 10; f '(t) = 0 t = ;

;

( ) ( )

;

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