Question

a equação da reta tangente a curva f(x)=x³-5x+1 noponto de abscissa 1 é

Answer 1

Encontremos o coeficiente angular... $m = f'(x)$.

$f'(x)=3x^2-5\\f'(1)=3-5\\\boxed{m=-2}$
 
 Portanto,

$\lim_{x\to\,p}\frac{f(x)-f(p)}{x-p}=f'(x)\\\\f(x)-f(p)=f'(x)(x-p)\\\\y=f'(x)(x-p)+f(p)\\\\y=f'(1)(x-1)+f(1)\\\\y=-2(x-1)+((1)^3-5\cdot(1)+1)\\\\y=-2(x-1)+(1-5+1)\\\\y=-2x+2-3\\\\\boxed{y=-2x-1}$