Начнём с последнего:
f(x) =6x² + 32x +2008
f⁾(x) = 12x +32
f⁾(x) = 0 ⇒12x + 32 = 0
12x = -32
x = -2 2/3
f(x) = 12x³ + 2x⁴
f⁾(x) = 36x² +8x³ = 4x²(9 + 2x)
f⁾(x)=0 ⇒x=0; x=-4,5
f⁾(x) <0 , x ∈(-∞; -4,5)<br>
f(x) = x⁵ - 3x⁴+ x, x= -2
f⁾(x) = 5x⁴ - 12x³ + 1
f⁾(-2) = 5*16 -12 *(-8) +1=90+96+1=187
f(x) =x¹⁰; f⁾(x) = 10x⁹
f(x) = -6x²; f⁾(x) = -12x
f(x) = 6x⁵ - 4x⁴ - 3x +27; f⁾(x) = 30x⁴ -16x³ - 3
f(x) = (x⁴ - 3)(x³ + 4) = x⁷ -3x³ +4x⁴ -12; f⁾(x) = 7x⁶-9x² + 16x³
f(x) = (3-2x)⁷; f⁾(x) =-2*7(3-2x)⁶ = -14(3-2x)6
f(x) =sin7x; f⁾(x) = 7cos7x
f(x) = cos²x; f⁾(x) =-2cosx*sinx = -sin2x
f(x) = cosx+ sinx; f⁾(x) = -sinx+cosx