1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Differentiation and finding tangent

  1. Sep 23, 2010 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations



    3. 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:
     
  2. jcsd
  3. Sep 23, 2010 #2
    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.
     
  4. Sep 23, 2010 #3
    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
     
  5. Sep 23, 2010 #4
    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: Sep 23, 2010
  6. Sep 23, 2010 #5
    Oo okay, thank you - just thought it was wrong considering the grad was 64 that's all.

    Thanks Susanne for checking :D
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook