- #1
ratio
- 2
- 0
Why does f attain its local maximum at r' in (p,q). Is it because we have f(x)<= f(r') for all x in (p,p+delta)?
Finding the maximum of a function
Click For Summary
SUMMARY
The discussion centers on the conditions under which a function f attains its local maximum at a point r' within the interval (p, q). It is established that f(r') is greater than or equal to f(x) for all x in the sub-interval (p, p + delta), confirming that the local maximum occurs at r'. The equality condition is also acknowledged, reinforcing the understanding of local maxima in calculus.
PREREQUISITES- Understanding of local maxima and minima in calculus
- Familiarity with the concept of intervals in real analysis
- Knowledge of function behavior and continuity
- Basic principles of optimization techniques
- Study the definitions and properties of local maxima and minima in calculus
- Explore the Mean Value Theorem and its implications for function behavior
- Learn about the first and second derivative tests for identifying extrema
- Investigate optimization techniques in real-valued functions
Students of calculus, mathematicians, and anyone interested in understanding optimization and function analysis.
Why does f attain its local maximum at r' in (p,q). Is it because we have f(x)<= f(r') for all x in (p,p+delta)?
- #2
- 20,815
- 28,447
We have equality, but, yes.ratio said:
- #3
ratio
- 2
- 0
Thanks for you answer^^
Similar threads
- · Replies 9 ·
- · Replies 1 ·
- · Replies 4 ·
High School
How do I invert this exponential function?
- · Replies 3 ·
Undergrad
Express the limit as a definite integral
- · Replies 16 ·
Undergrad
Limit as a function, not a value
- · Replies 15 ·
- · Replies 11 ·
- · Replies 25 ·
- · Replies 2 ·