Question

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

Answer 1

f(x) = a tan x + bx
f ' (x) = asec²x + b
f ' (π/4) = a(√2)² + b
3 = 2a + b ...................................................................(1)

f ' (π/3) = a(2)² + b
9 = 4a + b ..................................................................(2)
Dari persamaan (2) dan (1) didapat
4a + b = 9
2a + b = 3 -
2a = 6
a = 3
2a + b = 3 ⇔ 6 + b = 3 ⇒ b = 3-6=-3
 a+b = 3 - 3 = 0