The tangents to the curve with equation y = x^3-3x at the points A and B with x coordinates −1 and 4 respectively meet at the point C. Find the coordinates of the point C.

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 x-coordinate of -1. Hence, the slope of its tangent line is:

Find the y-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 x-coordinate of 4. Hence, the slope of its tangent line is:

Find the y-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 x:

We acquire:

Since one of our equations is y = 2, the y-coordinate is 2.

Hence, Point C is:

Step-by-step explanation:

y=x³-3x

so coordinates of C are (3,2)

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