El Paso, Amarillo, San Antonio are all cities that have a Influence​

Explanation:

step explanation:

We need to find the equation of the tangent lines of Points A and B.

Differentiate the equation:

\displaystyle \frac{dy}{dx}=3x^2-3

dx

dy

=3x

2

−3

Point A has an x-coordinate of -1. Hence, the slope of its tangent line is:

\displaystyle \frac{dy}{dx}\Big|_{x=-1}=3(-1)^2-3=0

dx

dy

∣

∣

∣

∣

x=−1

=3(−1)

2

−3=0

Find the y-coordinate of Point A using the original equation:

y(-1)=(-1)^3-3(-1)=2y(−1)=(−1)

3

−3(−1)=2

Hence, Point A is (-1, 2).

Thus, the tangent line at Point A is:

y-2=0(x-(-1))y−2=0(x−(−1))

Simplify:

y=2y=2

Point B has an x-coordinate of 4. Hence, the slope of its tangent line is:

\displaystyle \frac{dy}{dx}\Big|_{x=4}=3(4)^2-3=45

dx

dy

∣

∣

∣

∣

x=4

=3(4)

2

−3=45

Find the y-coordinate of Point B:

y(4)=(4)^3-3(4)=52y(4)=(4)

3

−3(4)=52

Thus, Point B is at (4, 52).

So, the tangent line at Point B is:

y-52=45(x-4)y−52=45(x−4)

Simplify:

y=45x-128y=45x−128

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:

2=45x-1282=45x−128

We acquire:

\displaystyle x=\frac{26}{9}x=

9

26

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

Hence, Point C is:

\displaystyle C=\left(\frac{26}{9}, 2\right)C=(

9

26

,2)

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