Equation of Tangent?

Question

consider the fucntion f(x)=2x^3+6x^2-4.5x -13.5. state the roots of this cubic and confim using the remainder theorem.
Roots : -1.5, -3, 1.5
(This is Done)

Here's the problem :-
then,taking the roots two at a time, find the equations of the tangent lines to the average of two of the three roots. Find where the tangent lines at the average of the two roots intersect the curve again?

I dont know how to get the eq. of tangent!

Answer 1

Find the first derivative

f'(x) = 6x² +12x - 4.5

The slope of the tangent at x = a is f'(a) and it passes through the point (a, f(a))

So you have enough information to get the equations of the tangents

eg Average of -1.5 and 1.5 = 0
f'(0) = -4.5 so slope of tangent at x = 0 is -4.5
f(0) = -13.5 so tangent passes through (0. -13.5)

Tangent is of form y = mx + b

ie y = -4.5x + b

When x = 0, y = -13.5
-13.5 = 0 + b

Thus equation of tangent is

y = -4.5x - 13.5

Answer 2

You need a math tutor.

Answer 3

neither do i
i jst press it on the calc