Question

Срочно, 50 баллов даю

Answer 1

$1)\ \ f(x)=x^2-2x+1\ \ ,\ \ x_0=1\\\\f'(x)=2x-2\ \ ,\ \ f'(x_0)=f'(1)=2-2=0\ ,\\\\f(x_0)=f(1)=1-2+1=0\\\\\boxed {\ y=f(x_0)+f'(x_0)(x-x_0)\ }\\\\y=0+0\cdot (x-1)\ \ \ \Rightarrow \ \ \ \underline {\ y=0\ }$

$2)\ \ f(x)=3x+x^2-5\ \ ,\\\\k=7\ \ \Rightarrow \ \ k=f'(x_0)=7\\\\f'(x)=3+2x\ \ ,\ \ f'(x_0)=3+2x_0=7\ \ ,\ \ \ 2x_0=4\ \ ,\ \ \underline {\ x_0=2\ }$

$3)\ \ f(x)=x^3-2x^2+2\ \ ,\ \ x_0=2\\\\\boxed {\ tg\varphi =k=f'(x_0)\ }\\\\f'(x)=3x^2-4x\ \ ,\ \ f'(x_0)=f'(2)=3\cdot 2^2-4\cdot 2=12-8=4\\\\\underline {\ tg\varphi =4\ }$