Verified answer

Уравнение касательной :

y = f(x₀) + f'(x₀)(x - x₀)

f(x) = 4x - Sinx + 1

f(x₀) = f(0) = 4 * 0 - Sin0 + 1 = 0 - 0 + 1 = 1

f'(x) = 4(x)' - (Sinx)' + 1' = 4 - Cosx

f'(x₀) = f'(0) = 4 - Cos0 = 4 - 1 = 3

y = 1 + 3(x - 0) = 1 + 3x

Ответ : y = 3x + 1