y_(0)=2^2=4
y`_(x)=y`_(t)/x`_(t)=(2*2^(2t)*ln2)/(-2^(-t)*ln2)=
=(2*2^(2t))/(-2^(-t))
y`(x_(0))=(2*2^(2))/(-2^(-1))/=-16
Уравнение касательной:
у-f(x_(0))=f`(x_(0))*(x-x_(0));
y-4=-16*(x-(1/2);
16x+y-12=0
Уравнение нормали
у-f(x_(0))=(-1/f`(x_(0)))*(x-x_(0));
у-4=(-1/16)*(х-(1/2))
2x-32y+127=0
y``_(x)=(y`_(x))`_(t)/x`_(t)=
=((2*2^(2t))`*2^(-t)-(-2^(-t))*2*2^t)/(-2^(-t))^2*(-2^(-t))*ln2=
=2*2^(2t)*(-2^(-t))*(2+1)/(-2^(-t))^3=
=6*2^(4t)
y``(x_(0))=y``(1)=96.