1. f'(x)=(4x³-2x-40)'=12x²-2
f'(3)=12*3²-2, f'(3)=106
2. y=10+sin3x
E(sinx)=[-1;1]
E(10+sin3x)=10+[-1;1]
E(10+sin3x)=[9;11]
3. 5sin²(3π/4)-3cos²(π/3)+tgπ=5*(√2/2)²-3*(1/2)²+0=5*(2/4)-3*(1/4)=10/4-3/4=7/4
4. f'(x₀)=tgα
f'(x)=(2x²-5x)'=4x-5
x₀=2
f'(2)=4*2-5, f'(x)=3
tgα=3