1. V

    Prove a function decreases.

    Prove that the function f(x) = logx(x+1) decreases on the interval (1,+infinity). How should I approach this proof? Thoughts?
  2. U

    when does this function grows and when it decreases?

    Hi there. I got this function, and I must find the intervals where it grows and when it decreases. Here it is: f(x)=x\ln^2(x) I found its derivative: f'(x)=\ln^2(x)+2ln(x) From here I see that it will always grows when x>1. But, what happends before it gets to x=1? How must I think this...
  3. S

    How do I know this series decreases or not?

    We're supposed to use the alternating series to say if this diverges or converges and if we do not know what it does using the alternating series test (regardless of what another test says) then we need to state that as well. However, the answer to the question is that it converges and since the...
  4. V

    f decreases most rapidly at Q

    Find a unit vector in the direction in which f decreases most rapidly at Q Thank u!
  5. U

    Show that a differentiable function f decreases most rapidly....

    at x in the direction opposite to the gradient vector, that is, in the direction of -Vf(x). I made up a function of two variables f(x, y) = ln(x^2 -y^3/2) and then calculated the gradient which came to 2x/(x^2 - y^3/2) and -3/2y^2/(x^2 - y^3/2). I then put in a value Vf (2, 1) and got the...
  6. K

    graph that increases or decreases

    A graph shows the entire function f(x) (0,2) (6,5). If the graph of f^-1(x) was sketched in the same figure, give your best description? My answe is The graph of f^-1(x) increases from 0 to 6. Is this right, thanks fo checking.