+0  
 
0
24
1
avatar

C. f(x)=8x2-4x+3 = 16x-4

 

use c. to find the tangent line at x=1. Where is there a horizontal tangent line?

Guest May 15, 2018
Sort: 

1+0 Answers

 #1
avatar+86645 
+1

The slope of the tangent line at  x  = 1  is   16(1) - 4   = 12

 

And at x  = 1, then  y  =  8(1) ^2  -4(1)  + 3   =  8 - 4 + 3  = 7

 

So...the equation of the tangent line is

 

y  = 12 (x - 1)  + 7

 

y = 12x  - 12 +  7

 

y  =12x - 5

 

Here's the graph : https://www.desmos.com/calculator/daj2o31drm

 

The horizontal tangent line will be tangent to the vertex.......it will have a slope of  0

So...we have that the x coordinate of the vertex is

 

16x - 4  = 0

 

16x  = 4

 

x  = 1/4

 

And when x  = 1/4, y  =  8(1/4)^2 - 4(1/4) + 3  =  1/2 - 1 + 3  =  2.5  = 5/2

 

So.....there is a horizontal tangent line at  ( 1/4, 5/2 )

 

 

 

cool cool cool

CPhill  May 15, 2018

6 Online Users

avatar
New Privacy Policy (May 2018)
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  Privacy Policy