Question

How do you find the equation of the secant line through the points where X has the given values: `f(x)=x^3-12x+1`; x=-3, x=3?

Answer 1

I found: `y=3x+1`

Explanation:

This is interesting....!
Let us find the coordinates `x,y` of the two point where your secant passes through the curve of your function;

We have the coordinates `x` and we need the `y`. To do that we evaluate the function in `x=3` and `x=-3`:
`f(3)=(3)^3-12*3+1=27-36+1=-8`
So the first point of our secant has coordinates (`3, -8`);

`f(3)=(-3)^3+12*3+1=-27+36+1=10`
So the second point of our secant has coordinates (`-3, 10`);

The equation of our secant can be found using the general relationship:

`(x-x_2)/(x_2-x_1)=(y-y_2)/(y_2-y_1)`
That with our data becomes:
`(x-(-3))/(-3-3)=(y-10)/(10-(-8))`
`(x+3)/-6=(y-10)/18`
`y=3x+1`

Graphically: