• Support PF! Buy your school textbooks, materials and every day products Here!

Tangent Lines

I need to find an equation for the tangent line to the graph of the function at the specified point, I had some trouble simplifing f(x) so that I can take the lim as x->0 which is the slope.

f(x) = Sqrt(x)/5 at (4,(2/5))
 

Answers and Replies

732
0
*Simply find the derivative of the curve at that point, and use point-slope to find the line.
[tex] f\left( x \right) = \frac{\sqrt x}{5} \Rightarrow f\,'\left( x \right) = \frac{1}{{10\sqrt x }} [/tex]

*To find the slope of the tangent line, simply calculate [itex] f\,' ( 4 ) [/itex]:
[tex] f\,'\left( 4 \right) = \frac{1}{{20}} [/tex]

*Next, just use point-slope to represent the tangent line, which I'll call [itex] y [/itex]:
[tex] \frac{{x - 4}}{{20}} = y - \frac{2}{5} [/tex]

And it's algebra from there :smile:
 
Last edited:
HallsofIvy
Science Advisor
Homework Helper
41,736
894
Victor Frankenstein said:
I need to find an equation for the tangent line to the graph of the function at the specified point, I had some trouble simplifing f(x) so that I can take the lim as x->0 which is the slope.

f(x) = Sqrt(x)/5 at (4,(2/5))

Are you saying that you are required to use the basic formula for the derivative: [itex] lim_{h->0}\frac{f(a+h)-f(a)}{h}[/itex] rather than the more specific formula (derived from that) that bomba923 used?

If so try multiplying both numerator and denominator of
[tex]\frac{\sqrt{a+h}-\sqrt{a}}{h}[/tex]
by
[tex]\sqrt{a+h}+ \sqrt{a}[/tex].
 

Related Threads for: Tangent Lines

  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
13
Views
2K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
2
Replies
31
Views
3K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
8
Views
2K
Top