There are no solutions to the equation f'(x) = 0. Extreme values can occur at points other than where the deriviative is zero. What are these other points?Nawz said:Homework Statement
Find the relative extrema of each function, if they exist. List each extremum along with the x-value at which it occurs. Then sketch a graph of the function.
25. f(x)=1-x2/3
Homework Equations
The Attempt at a Solution
f prime of (x)= -2/3x-1/3
-2/3x-1/3= 0
??
But x = 0 is not a solution of f'(x) = 0, and that's what you were looking for. Do you understand why x = 0 is an extreme point?Nawz said:Thanks for the help, I figured it out.
It was (x)=0 for f'(x) , idk why I couldn't see that. so when i put that in the original equation i got 1. So the x point was (0,1) . And then I found the remaning points on the graph and it was correct with the back of the book answer.
Please start a new thread.Nawz said:Thank you
If i have another questions, can i just ask here or should i make a new topic? It's the same type of questions just another problem?
Mark44 said:But x = 0 is not a solution of f'(x) = 0, and that's what you were looking for. Do you understand why x = 0 is an extreme point?
Please start a new thread.
Relative extrema in calculus refer to the points on a graph where the function has a local maximum or minimum value. These points are relative to a specific interval or range on the graph, rather than the entire graph.
To find the relative extrema of a function, you must first take the derivative of the function and set it equal to zero. Then, solve for the variable to find the critical numbers. Next, plug these critical numbers into the original function to find the corresponding y-values. The points where the y-values are the highest or lowest are the relative extrema.
Yes, a function can have multiple relative extrema. This occurs when the graph of the function has multiple peaks and valleys within a specific interval. These points can be identified by finding the critical numbers and determining which ones correspond to a local maximum or minimum value on the graph.
A relative maximum is the highest point on a graph within a specific interval, while a relative minimum is the lowest point on a graph within a specific interval. In other words, a relative maximum is the highest y-value and a relative minimum is the lowest y-value within a given range on the graph.
The relative extrema of a function can be used to optimize a process or find the maximum or minimum value of a quantity. For example, in economics, the relative extrema of a profit function can be used to determine the optimal production level for a company. In physics, the relative extrema of a velocity function can be used to find the maximum height of an object thrown into the air.