Answer:
Step-by-step explanation:
We need to find the equation of the tangent lines of Points A and B.
Differentiate the equation:
Point A has an <em>x-</em>coordinate of -1. Hence, the slope of its tangent line is:
Find the <em>y-</em>coordinate of Point A using the original equation:
Hence, Point A is (-1, 2).
Thus, the tangent line at Point A is:
Simplify:
Point B has an <em>x-</em>coordinate of 4. Hence, the slope of its tangent line is:
Find the <em>y-</em>coordinate of Point B:
Thus, Point B is at (4, 52).
So, the tangent line at Point B is:
Simplify:
Point C occurs at the intersections of the tangent lines of Points A and B. Set the two equations equal to each other and solve for <em>x: </em>
We acquire:
Since one of our equations is <em>y</em> = 2, the <em>y-</em>coordinate is 2.
Hence, Point C is: