Answer:
a) mt = -2
b) y=2-2x
Step-by-step explanation:
We have [tex]y=x-x^{3}[/tex] ⇒ [tex]f(x)=x-x^{3}[/tex] and we must find
a) The slope of the tangent line to the curve at the point (1,0)
b) The equation of the tangent line in part (a)
a) [tex]f(x)=x-x^{3}[/tex] with the point (1,0) then f'(x) [tex]=1-3x^{2}[/tex] the slope (mt) in x=1 is
f'(1)=[tex]1-3(1^{2})=1-3=-2[/tex] , m t= -2
b) mt=-2 at the point (1,0), knowing that the pending point model is:
[tex]y-y_{1}=m(x-x_{1})[/tex], we solve y-0 = -2(x-1) ⇒ y=-2x+2
