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Homework Help: Hints? Derivatives: Intervals, stationary points, logarithms, continuous functions

  1. Mar 2, 2010 #1
    hints??? Derivatives: Intervals, stationary points, logarithms, continuous functions

    1. The problem statement, all variables and given/known data

    Got any hints or anything?

    1. Suppose that f(x) = (x - 3)^4 ( 2x + 5)^5
    a) Find and simplify f ' ( x )
    b) Find stationary points of f
    c) Find exactly the intervals where f is increasing and intervals where f is decreasing

    2. Find the stationary points of g(x) = 2cos - sqrt(3)x , 0< _ x < _ 2pi and classify them (as local minimum, local maximum or neither).

    3. The temperature of the ground at a distance of d centimetres below the surface at a certain location can be modelled by g(t) = 16t + 11e^-0.00706dCOS(2(pi)(t) - 0.00706d-0.628)
    where t is the time in years since July 1.
    a) Find and interpret g(t) and g '(t) on sept 1 at ground level (d =0)
    b) Find and interpret g(t) and g '(t) on sept 1 at 3 m below ground level.

    4. Let h be continuous, differentiable function such that g(3) = -7, g(-7) = 3, g '(3) = 2, and g '(-7) = 4

    a) Find (g^-1)(3) and (g^-1) '(3)
    b) Find an equation for the tangent line to the graph of g^-1(x) at x=3
    c) With only the information, what is your best estimate of (g^-1)(4) ?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 2, 2010 #2

    tiny-tim

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    Hi Carl_M! :smile:

    (have a pi: π and a square-root: √ and a ≤ and try using the X2 tag just above the Reply box :wink:)

    Show us what you've tried, and where you're stuck, and then we'll know how to help!

    Start with 1. :smile:
     
  4. Mar 2, 2010 #3
    Re: hints??? Derivatives: Intervals, stationary points, logarithms, continuous functi

    1. a) d/dx (( x-3)^4(2x+5)^5)

    = (2x+5)^5(d/dx((x-3)^4)) + (x-3)^4(d/dx((2x+5)^5)
    =4(x-3)^3(2x+5)^5(d/dx(x-3)) +5(x-3)^4(2x+5)^4(d/dx(2x+5))
    =4(x-3)^3(2x+5)^5 +10(x-3)^4(2x+4)^4 = 0

    X=3 , X = 5/9 , -5/2

    How would I get the increasing/decreasing?

    c ) Would it be Increase on [ -oo, 5/9] and decrease on [5/9, oo] ?
     
    Last edited: Mar 2, 2010
  5. Mar 2, 2010 #4

    tiny-tim

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    Sorry, that's too difficult to read :redface:

    please use the X2 tag just above the Reply box :smile:
     
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