Question

Find the equations of the tangent to the curve y=(x^{​​​​​​3​​​​​​​}​-1)(x-2) at the points where the curve intersects at the x axis

Answer 1

The curve intersects x axis means at y=0
So
For y=0 x is 2 and 1 from equation
The curve cuts the x axis at points with co-ordinates (2,0);(1,0).
So now differentiate the equation as you know it’s a polynomial function hence it’s differentiable...
Differentiating it you will find the slope of the tangent at those points..which are..
slope,m=7 for (2,0).
m= -3 for (1,0).
So you can now write the equations knowing the poinrs and slopes of the corresponding lines.