Question

Find the angle between the tangents to the graph of the function $y=x^3-x$ at points with abscissas $x_1=-1and{x}_2=1.$

Answer 1

$y=x^3-x$

$x_1=-1$ , $y_1=0$

$x_2=1$ , $y_2=0$

equation of tangents

$\frac{y-y_1}{x-x_1}=y_1^{\prime }=3x_1^2-1$

slope: $y^1=3x^2-1$

slope at $(x_1,y_1);y_1^{\prime }=2$

at $(x_2,y_2);y_2^{\prime }=2$

angle between the tangent :$0$

($\therefore$ same slope)