Question

Given f(x)=x^3-2, find the equation of the secant line passing through (-4,f(-4)) and (2,f(2))

Answer 1

Given:

The function is

`f(x)=x^3-2`

The secant line passing through (-4,f(-4)) and (2,f(2)).

To find:

The equation of the secant line.

Solution:

We have,

`f(x)=x^3-2`

At x=-4,

`f(-4)=(-4)^3-2`

`f(-4)=-64-2`

`f(-4)=-66`

At x=2,

`f(2)=(2)^3-2`

`f(2)=8-2`

`f(2)=6`

The secant line passes through the points (-4,-66) and (2,6). So, the equation of the secant line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-(-66)=(6-(-66))/(2-(-4))(x-(-4))`

`y+66=(6+66)/(2+4)(x+4)`

`y+66=(72)/(6)(x+4)`

On further simplification, we get

`y+66=12(x+4)`

`y+66=12x+48`

`y=12x+48-66`

`y=12x-18`

Therefor, the equation of the secant line is
`y=12x-18`.