Calculas

posted by .

Find any critical numbers of the function. (Enter your answers as a comma-separated list.)

g(t) = t sqrt6 − t , t < 13/3


I don't even know how to start out!

  • Calculas -

    I will assume you meant

    g(t) = t √(6-t) = t(6-t)^(1/2)

    g'(t) = t (1/2)(6-t)^(-1/2) (-1) + (6-t)^(1/2) using the product rule
    = 3)t-4)/(2√(6-t) )
    =0 for any max/min values of the function

    t/(2(6-t)^(1/2) = (6-t)^(1/2)
    t = 2(6-t)
    t = 12 - 2t
    3t = 12
    t = 4
    so g(4) = 4√(6-4) = 4√2

    to see if there are any points of inflection
    differentiate 3(t-4)/(2√(6-t) ) , set that result equal to zero and solve for t
    (hint: there are no points of intersection)
    You should get a second derivative of 3(t-8)/(4(6-t)^(3/2 )
    which when you set equal to zero will give an answer of
    t = 8
    BUT, t=8 is outside the domain of our function, so ... No Solution.

    y-intercepts ? , let t =0
    y = 0√6 = 0 , the origin (0,0)

    any t-intercepts?
    t(6-t)^(1/2) = 0
    t = 0 or t = 6

    look at the graph .....
    http://www.wolframalpha.com/input/?i=t%286-t%29%5E%281%2F2%29

    ignore the imaginary part of the graph (the red line)
    the point (4,4√2) is a maximum point

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Find any critical numbers of the function. (Enter your answers as a comma-separated list.) g(t) = 3t ln t
  2. Calculus

    Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) h(p) = (p − 2)/(p^2 + 9)
  3. Math

    Find any critical numbers of the function. (Enter your answers as a comma-separated list.) g(x) = x^7 − 7x^5 Honestly, I have no idea how to find the critical number!
  4. Business

    Given y = 4x3 − 48x2 + 5. (a) Find the critical values of the function. (Enter your answers as a comma-separated list
  5. Math

    Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x)=x^(4/5)(x − 6)^2
  6. pre-calculas

    Find the slant asymptote, if any, of the rational function. Do not graph the function. (Enter your answers as a comma-separated list of equations. If an answer does not exist, enter DNE.) f(x) = x2 − 2x + 15 _____________ x + …
  7. Calculus 1

    Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) h(t) = t^(3/4) − 3t^(1/4)
  8. Calculus 1

    Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) F(x) = x^4/5(x − 1)^2
  9. Calculus 1

    Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x^(5)e^(-6x)
  10. Pre-Calculus

    f(x) = cos(x) on the interval [−2π, 2π] (a) Find the x-intercepts of the graph of y = f(x). (Enter your answers as a comma-separated list.) (b) Find the y-intercepts of the graph of y = f(x). (Enter your answers as …

More Similar Questions