The book is correct.jorcrobe said:Homework Statement
F(x)=(x^2)/(x+1)
Find critical points
Find local maxima & minima
Homework Equations
None
The Attempt at a Solution
F'(x) = x(x+2)/(x+1)^2
crit points: -2,0,-1
f(-2) = -4
f(0) = 0
f(-1)=undef
My book is telling me that f(0) is the minimum, and f(-2) is the maximum. I see it as the other way around. Which way is right? Explanations? Thank you!
jorcrobe said:Homework Statement
F(x)=(x^2)/(x+1)
Find critical points
Find local maxima & minima
Homework Equations
None
The Attempt at a Solution
F'(x) = x(x+2)/(x+1)^2
crit points: -2,0,-1
f(-2) = -4
f(0) = 0
f(-1)=undef
My book is telling me that f(0) is the minima, and f(-2) is the maxima. I see it as the other way around. Which way is right? Explanations? Thank you!
A local maximum is a point on a graph where the function reaches its highest value within a specific interval, but it may not be the highest value on the entire graph.
A local minimum is a point on a graph where the function reaches its lowest value within a specific interval, but it may not be the lowest value on the entire graph.
Local maxima can be identified by looking for peaks in the graph where the slope changes from positive to negative. Local minima can be identified by looking for valleys in the graph where the slope changes from negative to positive.
Local maxima and minima are important for understanding the behavior of a function and determining critical points. They can also be used to find the optimal solution in optimization problems.
A local maximum or minimum is a point that is higher or lower than the points directly next to it, respectively. A global maximum or minimum is the highest or lowest point on the entire graph. Local extrema are found within a specific interval, while global extrema are found on the entire graph.