(388.8K) [189] 5. 접선의 방정식

5.

1 / 3 MATHMEDIC .

101127 ( ) # 4636

, ?

y= e^x (1, e) y= 2 x − k

k

1 e

1 2

e²

1 3

e⁴ 1

4 1 + e

1 5

1 + e² 1

2

110921 # 4510

.

, .

f(x) = x − (a + 2)x + ax^{3 2} y= f(x)

(t, f(t)) y g(t) g(t)

(0, 5) a

151114 # 1377

. ,

.

,

.

, ?

[13 ∼ 14] a > 3 a y= a^x−1 y= 3^x

P P x k 13 14

P y= 3^x x A P

y= a^x−1 x B

H(k, 0) AH= 2BH a

1 6 2 7 3 8 4 9 5 10

161107 # 1460

,

?

y= 3e^x−1 A O OA

1 6 2 7 3 2 2

4 3 5 10

5

160910 # 1433

y= ln 5x (51 ), 0 y ?

1 −

2

5 2 −2 3 −

2 3

4 −1 5 −

2 1

170611 # 1674

, ?

y= ln(x − 3) + 1 (4, 1) y= ax + b a, b a+ b

1 −2 2 −1 3 0 4 1 5 2

7

171115 # 1648

, .

?

y= 2e^−x P(t, 2e )^−t (t > 0) y

A P y B

APB t

1 1 2

2

e 3 2 4 2 5 e

3 / 3 MATHMEDIC .

181121 # 2284

,

.

  .

.

?

t [1, ∞) f(x)

f(x) ={ln x

−t + ln x

(1 ≤ x < e) (x ≥ e)

g(x) y= g(x) h(t)

1 x (x − e){g(x) − f(x)} ≥ 0

h(t) a h(a) =

e+ 2 1 h^′( ) × h (a)2e

1 _′

1 (e + 1)²

1 2

e(e + 1) 1

3 e²

1 4

(e − 1)(e + 1) 1

5 e(e − 1) 1

9

180616 # 1589

.

.

, ?

k f(x)

f(x) ={ x²+ k ln(x − 2)

 (x ≤ 2)  (x > 2)

t y= x + t y= f(x)

g(t) g(t) t = a a

k

1 −2 ² −

4

9 3 −

2 5

4 −

4

11 5 −3

1 . 2 . 13 3 . 4 . 5 .

6 . 7 . 8 . 9 .