Hello! I need to determine the saddle point of several functions. I have already calculated it several times but still cannot get the result. Can someone correct and explain the error in my calculation: f(x) = 2x^3 + 3x^2 + 12 f`(x) = 6x^2 + 6x f“(x) = 12x + 6 f“`(x) = 12 f“(x)…
Hey, this is the following graph of the function: f(x)=3x^(4)+4x^(3). Could one now say that at the point (0/0) there is both an inflection point and a saddle point, i.e.: SP(0/0) and WP(0/0)? Is this correct? Thank you.
Hey, is the saddle point also a turning point? Thank you.
Hey, I was asked to determine the peak and trough points of a certain function using the sign change criterion. I did just that. Could someone help me with the second part of the task?: How do I describe the course at the point X=0 (of f) without seeing the graph? Thank you.
Hey, is a saddle point also an extreme point? Thank you.
Hey, the following derivative function is given and I should now specify the intervals and its monotonicity. This is the derivative graph: Would this solution be correct: I1: -~;7= monotonically decreasing, since f'(x)=<_0. I2: 7;+~= strictly monotonically decreasing, since f'(x)=>0. Or would this solution be correct: I1:-~;7= strictly monotonically decreasing, since f'(x)=<0. I2: 7;+~= strictly…
Hey, I've actually been searching for this for a really long time, and everyone is getting different answers. What's your opinion, or which of these is actually true? I think it's true that, for example, the rule x1<x2 and f(x1)<f(x2) isn't violated. But on the other hand, the function is still horizontal at one point,…
Hey, which of these two things is true? Thank you.
Hey, the task is: Give a reasoned explanation for the monotonicity behavior in the individual intervals! This is the following function: These are my solutions: Which of my solutions is correct? Thank you.
Hey, the function is: f(x)=-x^(5)-x. I've already started by taking the first derivative and then setting it to zero. Now I've solved everything for zero. But there's no solution here, and the sufficient condition that x=0 is no longer met. What do I do next? Thank you.
Hey, I should calculate the saddle point of the following function “f(x)=2x^(3)+4” and then determine its monotonicity. Are my following calculations correct?: Is the last sentence of my answer also correct? Thank you.
Hey, I should determine the intervals of the following graph and determine its monotonicity. This is the corresponding graph: This is how I would have divided the intervals: I1: -~;-1.1 I2: -1.1;+1.1 I3: +1.1;+~ This is how I would determine the monotony in the three intervals: I1: strictly monotonically increasing I2: strictly monotonically decreasing I3:…