Уравнение касательной y=f(x0)+f`(x0)*(x-x0)
255
1)f(x)=x²+1
f(0)=1
f`(x)=2x
f`(0)=0
y=1+0(x-0)=1
f(1)=1+1=2
f`(1)=2
y=2+2(x-1)=2+2x-2=2x
2)f(x)=x³-1
f`(x)=3x²
f(-1)=-1-1=-2
f`(-1)=3*1=3
y=-2+3(x+1)=-2+3x+3=3x+1
f(2)=8-1=7
f`(2)=3*4=12
y=7+12(x-2)=7+12x-24=12x-17
256
1)y=1+cosx
f`(x)=-sinx
f(0)=1+1=2
f`(0)=0
y=2+0*(x-0)=2
f(π/2)=1+0=1
f`(π/2)=-1
y=1-1(x-π/2)=-x+1-π/2
2)f(x)=2sinx
f`(x)`=2cosx
f(π/2)=2*1=2
y`(π/2)=2*0=0
y=2+0*(x-π/2)=2
f(π)=2*0=0
f`(π)=2*(-1)=-2
y=0-2(x-π)=-2x+2π