Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Given:
The function is
[tex]f(x)=x^3-2[/tex]
The secant line passing through (-4,f(-4)) and (2,f(2)).
To find:
The equation of the secant line.
Solution:
We have,
[tex]f(x)=x^3-2[/tex]
At x=-4,
[tex]f(-4)=(-4)^3-2[/tex]
[tex]f(-4)=-64-2[/tex]
[tex]f(-4)=-66[/tex]
At x=2,
[tex]f(2)=(2)^3-2[/tex]
[tex]f(2)=8-2[/tex]
[tex]f(2)=6[/tex]
The secant line passes through the points (-4,-66) and (2,6). So, the equation of the secant line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-66)=\dfrac{6-(-66)}{2-(-4)}(x-(-4))[/tex]
[tex]y+66=\dfrac{6+66}{2+4}(x+4)[/tex]
[tex]y+66=\dfrac{72}{6}(x+4)[/tex]
On further simplification, we get
[tex]y+66=12(x+4)[/tex]
[tex]y+66=12x+48[/tex]
[tex]y=12x+48-66[/tex]
[tex]y=12x-18[/tex]
Therefor, the equation of the secant line is [tex]y=12x-18[/tex].
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
