Derivatives: Logarithmic Function help

  • Thread starter Slimsta
  • Start date
  • #1
190
0

Homework Statement


Find an equation of the tangent line to the curve
[tex]$\displaystyle \Large y = (2 x^2+5 )\ln (4 x^2-3 )+7$[/tex]
when x = 1.


Homework Equations


[tex]$\displaystyle \Large y = f'(x_0)(x-x_0)+f(x_0).$[/tex]


The Attempt at a Solution


the fact that the tangent line to the curve y = f(x) when x = a is given by
[tex]$\displaystyle \Large y = f'(x_0)(x-x_0)+f(x_0).$[/tex] and a=1

f(1) = 7
f'(1) = 48
tangent line => y=48x-41
right?

this is how i did it:
f(1) = 7 (just plug in the number in f(x)
for f'(1),
i did:
[tex]$\displaystyle \Large dy/dx = 4x\ln (4 x^2-3 )+(1/(4 x^2-3 ) )* 8x * (2 x^2+5 )$[/tex]
and pluged in 1 and got 48.

then found the tangent line by doing y=mx+b ==> y=48x+b ==> 7=48*1+b ==> b= -41
y=48x-41

is everything correct so far?
 

Answers and Replies

  • #2
35,028
6,774
Everything looks fine, but I didn't check all of your arithmetic. Your value for f(1) is correct and your derivative is correct, but I didn't confirm it for f'(1).
 
  • #3
867
0
I get another number for f'(1), not 48.
 
  • #4
190
0
I get another number for f'(1), not 48.

omg.. what a stupid mistake... bhahaha, its 56 actually..
kk i got it lol.
thanks!
 

Related Threads on Derivatives: Logarithmic Function help

Replies
4
Views
2K
  • Last Post
Replies
1
Views
1K
Replies
2
Views
1K
  • Last Post
Replies
4
Views
2K
Replies
8
Views
2K
Replies
9
Views
2K
Replies
2
Views
2K
Replies
3
Views
847
Top