Write this as an equation, and use parentheses.mathpat said:Homework Statement
x^2 / x-1. Identify any asymptotes, extrema and points of inflection.
As an equation, this is f'(x) = x(x-2)/(x-1)2.mathpat said:Homework Equations
The Attempt at a Solution
I am stuck trying to derive my first derivative. My first derivative equals x(x-2)/(x-1)^2.
Your answer is correct, and this can be verified by calculating the derivative using the technique that Zondrina suggested.mathpat said:I tried to use the quotient rule again using while incorporating the chain rule and after multiple attempts I kept resulting with 2 / (x-1)^3.
Any suggestions?
The sign of f'' changes at x = 1. If x < 1, f''(x) < 0, and if x > 1, f''(x) > 0. Does this mean that there is an inflection point at x = 1? Why or why not?mathpat said:I see... so basically that means there is no point of inflection since I can not set that equation equal to zero and solve?
mathpat said:By the way, I appreciate both of your help.
A point of inflection is a point on a graph where the curve changes from being concave upwards to concave downwards, or vice versa. In other words, it is the point where the curvature of the graph changes.
To find the point of inflection for x^2/x-1, we need to take the second derivative of the function and set it equal to zero. This will give us the x-value of the point of inflection. Then, we can plug this x-value back into the original function to find the corresponding y-value.
A point of inflection is significant because it indicates a change in the direction of the curve. It can also help us identify the minimum or maximum points of a function.
Yes, a function can have more than one point of inflection. This occurs when the curve changes direction multiple times, resulting in multiple points where the curvature changes.
To graph a function with a point of inflection, we first need to find the x and y values of the point of inflection. Then, we can plot these coordinates on the graph and use the direction of the curve to determine the shape of the graph on either side of the point of inflection.