Bab 2 Ruko 2 Matematika Kelas XII Sukino no 22

Soal dan Pembahasan Matematika Sukino
Kelas XII
Sukino Kelas XII
Kunci Jawaban Matematika Kelas XII Peminatan
Bab 2 Turunan Fungsi Trigonometri
RUKO 2
Bag A

22. Jika f(x) = a tan x + bx dan f ' (π/4) = 3, f '(π/3) = 9, maka a + b = ...

a. -6
b. -3
c. 0
d. 3
e. 6

Jawaban : C

f(x) = a tan x + bx

u = a tan x
u ' = a sec² x

v = bx
v ' = b

f(x) = a tan x + bx
f ' (x) = a sec² x + b

f '(π/4) = a sec² (π/4) + b

3 = a . 1/cos² (π/4) + b

3 = a . 1/(1/2 √2)² + b
3 = a . 2 + b
3 = 2a + b
b = 3 - 2a


f '(π/3) = a sec² (π/3) + b
9 = a . 1/cos² (π/3) + b
9 = a . 1/(1/4) + b
9 = a . 4 + b
9 = 4a + b

9 = 4a + (3 - 2a)
9 = 2a + 3
6 = 2a
a = 3

b = 3 - 2a
b = 3 - 2.3
b = 3 - 6
b = -3

a + b = 3 + (-3) = 0



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