Question

Consider the curve y = x − x3. (a) Find the slope of the tangent line to the curve at the point (1, 0). (b) Find an equation of the tangent line in part (a).

Answer 1

Answer:

a) mt = -2

b) y=2-2x

Step-by-step explanation:

We have $y=x-x^{3}$  ⇒  $f(x)=x-x^{3}$ 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) $f(x)=x-x^{3}$ with the point (1,0) then f'(x) $=1-3x^{2}$ the slope (mt) in x=1 is

f'(1)=$1-3(1^{2})=1-3=-2$  ,  m t= -2

b) mt=-2 at the point (1,0), knowing that the pending point model  is:

$y-y_{1}=m(x-x_{1})$, we solve y-0 = -2(x-1) ⇒ y=-2x+2