1. Find the equation of the tangent line to the parabola y = x^3 at the point P(2,8). Use x = 2.1, 2.01, 2.001, 2.0001, 2.00001; 1.9,1.99, 1.999,1.9999, 1.99999 to find slope.

a) Equation of the tangent of the parabola

12 x - y -16=0

b)

slope of the tangent  at x=2.1

slope of the tangent  at x=2.01

Step-by-step explanation:

Step(i):-

Given parabola  y = x³  ....(i)

Differentiating equation (i) with respective to 'x'

slope of the tangent

Step(ii):-

Equation of the tangent of the parabola

y-8 = 12 (x -2)

12 x - 24 -y +8 =0

12 x - y -16=0

b)

slope of the tangent  at x=2.1

slope of the tangent  at x=2.01

Mantle

Step-by-step explanation:

I think its mantle