Post a New Question

ap calculus

posted by on .

a particle moves along the x axis in such a way that its acceleration at time t, t>0 , is given by x(t)= (ln x)^2. at what value of t does the velocity of the particle attain its maximum

  • ap calculus - ,

    velocity has max when acceleration is zero
    I assume x(t) = (ln t)^2 which is zero at t=1.

  • ap calculus - ,

    Assuming the function is
    then t has a vertical asymptote at x=0.
    which explains why the domain of x(t) is set at x>0.

    To find the maximum, we need to find
    and x'(t)=0 at t=1.
    Check if maximum or minimum by finding x"(t)=2/t^2 - 2ln(t)/t
    x"(1)=2 >0
    Hence t=1 is a minimum.

    Therefore, the function has no maximum, as it increases indefinitely as t inreases for t>1.

Answer This Question

First Name:
School Subject:

Related Questions

More Related Questions

Post a New Question