1)
2) f(x) = x²+x, xo = 1.
f'(x) = 2x+1,
f'(xo) = 2*1+1 = 3.
3) S(t) = t²-2t, to = 3.
V = S'(t) = 2t-2,
V(t=3) = 2*3-2 = 6-2 = 4 м/с.
4.1) у = х². хо = 1, х1 = 1,6.
к = Δу/Δх.
уо = 1, у1 = 2,56.
Δу = 2,56-1 = 1,56,
Δх = 1,6-1 = 0,6.
к = 1,56/0,6 = 2,6.
4.2) у(кас) = f'(xo)*(x-xo)+f(o). xo = 1.
f'(xo) = 2*1 = 2.
f(xo) = 1² = 1.
у(кас = 2(x-1)+1 = 2x-2+1 = 2x-1.