Intermediate Value Theorm:
In order to prove some "c value equals k," using the intermediate value theorem, use these steps:
1. f(x) is continuous on given domain.
2. f(a) < 0 and f(b) > 0 or f(b) < 0 and f(a) > 0
3. By intermediate value theorem, there exists a value such that f(c)=k
4. To find "c," set f(x)=0 than find those values.
1. f(x) is continuous on given domain.
2. f(a) < 0 and f(b) > 0 or f(b) < 0 and f(a) > 0
3. By intermediate value theorem, there exists a value such that f(c)=k
4. To find "c," set f(x)=0 than find those values.
Problem 1 and solution:
Problem 2 and solution:
Mean Value Theorm and Rolle's theorem, a special case of MVT
Problem 1 and solution: Prove that the function satisfies the three hypotheses of Rolle's theorem, than find the numbers that satisfy it.
Problem 2 and solution: Rolle's theorem.
Problem 1 and solution: Verify that the function satisfies the hypotheses of the mean value theorem on the given interval. Then find all the values that satisfy it.
Problem 2 and Solution: Mean value theorem