Question
Asked Dec 14, 2019
4 views

Find the points on the graph of the function that are closest to the given point.

 

f(x) - х2 - 8, (0, —6)
(smaller x-value)
(х, у)
(x, y) =
(larger x-value)
%3D
help_outline

Image Transcriptionclose

f(x) - х2 - 8, (0, —6) (smaller x-value) (х, у) (x, y) = (larger x-value) %3D

fullscreen
check_circle

Expert Answer

Step 1

Given:

help_outline

Image Transcriptionclose

f (x) = x² -8 (0,-6) Let y = x -8 .[1]

fullscreen
Step 2

Distance from point (0, -6) and (x, y) is:

help_outline

Image Transcriptionclose

d = (x-o0)° +(y-(-6)) d= (x-0)° +(y+6) d = (x-0)* +(x` -8+6) d = (x} +(x° - 2)° [y =x* -8] Let F(x) = x² +(x² – 2)*

fullscreen
Step 3

Differentiate F(x) with respe...

help_outline

Image Transcriptionclose

F(x)=x° +(x° -2)* F'(x) = 2x + 2-(x² – 2)· 2.x F'(x) = 2x + 4.x(x² - 2)

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Derivative