Differentiation and finding tangent

  • Thread starter Maatttt0
  • Start date
  • #1
37
0

Homework Statement



Find the equation of the tangent to the curve y = x2(x + 1)4 at the point P(1,16)

Homework Equations





The Attempt at a Solution



dy/dx x2(x + 1)4

= (x + 1)3((x + 1)2x + 4x2)

= (x + 1)3(6x2 + 2x)

= (x + 1)3(2x)(3x + 1)

Subst. 1 in to find grad.

(1 + 1)3(2)(3 + 1)

= 64

Seems wrong..

y - 16 = 64(x - 1)

y = 64x - 48

I think it's probably wrong, just so confused - can someone give me a hand please? Much appreciated :smile:
 

Answers and Replies

  • #2
317
0

Homework Statement



Find the equation of the tangent to the curve y = x2(x + 1)4 at the point P(1,16)

Homework Equations





The Attempt at a Solution



dy/dx x2(x + 1)4

= (x + 1)3((x + 1)2x + 4x2)

= (x + 1)3(6x2 + 2x)

= (x + 1)3(2x)(3x + 1)

Subst. 1 in to find grad.

(1 + 1)3(2)(3 + 1)

= 64

Seems wrong..

y - 16 = 64(x - 1)

y = 64x - 48

I think it's probably wrong, just so confused - can someone give me a hand please? Much appreciated :smile:

You should plug it into the derivative formula

[tex]f'(x) = \lim_{h \to 0}\frac{f(x+h) - f(x)}{h}[/tex]

and put this into you Calculator...

and use the good old Tangent formula.

[tex]y = f(a) + f'(a)(x-a) [/tex] where you take the derivative at x = a.
 
  • #3
37
0
Thank you for your reply, Susanne, it's just that I've never seen the tangent formula before :S

Also my homework is based around the idea of differentiating so I was wondering if I was going in the right direction :S
 
  • #4
317
0
Thank you for your reply, Susanne, it's just that I've never seen the tangent formula before :S

Also my homework is based around the idea of differentiating so I was wondering if I was going in the right direction :S

You derivative is correct.

But you can use the definition of the derivative and graphical Calculator to check your result.

and your userage of the tangent formula looks to be okay too :)
 
Last edited:
  • #5
37
0
Oo okay, thank you - just thought it was wrong considering the grad was 64 that's all.

Thanks Susanne for checking :D
 

Related Threads on Differentiation and finding tangent

  • Last Post
Replies
2
Views
1K
Replies
8
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
5K
Replies
8
Views
2K
Replies
1
Views
2K
Replies
7
Views
11K
Replies
5
Views
562
  • Last Post
Replies
6
Views
5K
Top