Recent content by yli

I think that Krylov has gotten what I was attempting to do, I was confused about it myself. In the case of drawing the graph of \[\frac{dP}{dt}=rP(K−P)−H.\] with respect to P, could someone tell me what would change? For the first graph, I got an upside down U-shape, and the question that I am...

So if I were to graph dp/dt as a function of P, how would I find the critical values? Would I just set this derivative to 0? Also, if a new constant is introduced into this, how would I find the derivative? The equation would change to \[\frac{dP}{dt}=rP(K-P)-H. \]

Would it end up being rK+2rP? Or did I factor wrong?

Hi, so I am trying to find the derivative of this function. \[ \frac{dP}{dt}=rP(K-P), \] r and K are positive constants describing the natural growth rate and carrying capacity of the population, respectively. I was trying to find the derivative, and I suppose that I am supposed to apply the...

Sorry, this is where I am stuck. The algebra is starting to confuse me a bit more so than usual. Could I get a hint of how I am supposed to find the critical values?

I believe that these two critical points do not exist on the graph for this function since the domain is restricted to values of x greater than 0. Also because the values of x have to be greater than 0, I am assuming that this function is always increasing. If this is correct, how would I go...

Hmmm, this is the part I was confused about because, critical points are where the function is equal to 0. When I set the function to 0, I am lost about what I am supposed to do next, \[\dfrac{(a-b)cdx^{d-1}}{(c+x^d)^2}=0 \] \[(a-b)cdx^{d-1}=0 \] I thought about dividing (a-b) from both sides...

Oh, that was a silly mistake. Once I factored I got \[g\prime(x)=\dfrac{(a-b)cdx^{d-1}}{(c+x^d)^2}\] I also tried to find the second derivative from this as well, would it be \[g\prime\prime(x)=\dfrac{(a-b)cd(c+x^d)(x^{d-2}((d-1))(c+x^d)-2dx^d))}{(c+x^d)^4} \] I am a bit confused about how I...

Since bc is a constant, I am assuming that it will become 0, and so the derivative of the first part should be \[(adx^{d-1})\] Then the derivative of the second part I am assuming is \[(x^{d-1})\] Sorry I am really bad at this and therefore still somewhat confused. Would this be correct...

Hi, I am having some trouble with this problem. I have completed part a but I am stuck on part b and c. I used the quotient rule to try and find the first derivative, but I am unsure if I have done so correctly. This is my work for part b so far...