Suppose that the cubic function f(x)=(x-a)(x-b)(x-c) has three distinct zeroes: a, b, c. Prove that a tangent line drawn at the average of the zeroes a and b intersect the graph of f at the third zero?
2 Answers
See below.
Explanation:
Given
the tangent line at
where
now the intersection between the tangent line and
or after simplifications
and as we can observe
See below:
Explanation:
Thus, the slope of the line joining the point
Now, the derivative of
So, the slope of the tangent to the curve at the point
Thus the tangent at the point