Question

Найти значение производной в точке x0:
A) f(x)=7x^2-56x+8 при x0=4
Б) f(x)4x/x^2+4 при x0=0
В) f(x)=(x^2+1)(x^3-2) при x0=1
Г) f(x)=3x*sinx при x0=Π/3

Answer 1

1) f'(x) = 14x -56
f'(4) = 14*4 -56 = 56 - 56 = 0
2) f'(x) = (4(x² +4) - 4x*2x)/(x² +4)² = (4x² +16 -8x²)/(x² +4)² = (16 - 4x²)/(x² +4)²
f'(0) = 16/16 = 1
3) f'(x) = 2x(x³ -2) + (x² +1)*3x² = 2x⁴-2x +3x⁴ + 3x² = 5x⁴ + x²
f'(1) = 5*1 + 1 = 6
4) f'(x) = 3Sinx + 3x*Cosx
f'(π/3) = 3Sinπ/3 + 3*π/3*Cosπ/3 = 3*√3/2 + 3*π/3*1/2 = 3√3/2 +3π/2