AP Calc BC: Unit 5 CORRECT 100%
The Mean Value Theorem (MVT) - ANSWERIf f is continuous AND differentiable on
the closed interval [a, b], then there exists at least one number c in (a, b) where
IROC = AROC
What happens when you mathamatically find the critical point but its undefined in the
euqation? - ANSWERIts not an critical point bc it means it a asymptote
How do you find the critical point if given the derative - ANSWERJust set it to 0 and
Make the sign chart
How do you find icnreasing or decreaing - ANSWER
Conditions for MVT and what to look for - ANSWERmust be continous and
differentiable so now breaks, sharp corners, etc
- Look for derivative value, not the function value and questions about the ROC of
the function given in the table
T or F: Polynomials are always continuous and differentiable - ANSWERT
How to use MVT - ANSWER1. Check conditions
2. Find Aroc
3. Set number found for AROC to the deriative (IROC) and solve for x
Intermediate Value Theorem (IVT) - ANSWERIf f is continuous on the closed interval
[a,b] and k is any number between f(a) and f(b), then there is at least one number c
in [a,b] such that f(c)=k
What to look for for IVT - ANSWERIf its continous, the fuction value not the derative,
and questions about a function value not found in the table.
What could help us determine the interals where f(x) is increasing and decreasing -
ANSWERROC/derivative
Critical points/values - ANSWERA horizontal tangnet or corner/cusp
If f(x) is defined at x=c then f(x) has a crtical point at x = c if f'(c) = 0 or f'(c) is
undefniend
How to find a critical point given f(x) - ANSWER1. Find derative and set it equal to 0.
2. Create a sign chart to test
1st Derivative Test - ANSWERLet c be critical # of a function f that is cont. on open
interval I containing c. If f is differentiable on interval, except possibly at c⇒f(c) is
classified as:
1. If f'(x) changes from - to + at c, then f has rel. min at (c,f(c))
2. If f'(x) changes from + to - at c, then f has rel. max at (c,f(c))
The Mean Value Theorem (MVT) - ANSWERIf f is continuous AND differentiable on
the closed interval [a, b], then there exists at least one number c in (a, b) where
IROC = AROC
What happens when you mathamatically find the critical point but its undefined in the
euqation? - ANSWERIts not an critical point bc it means it a asymptote
How do you find the critical point if given the derative - ANSWERJust set it to 0 and
Make the sign chart
How do you find icnreasing or decreaing - ANSWER
Conditions for MVT and what to look for - ANSWERmust be continous and
differentiable so now breaks, sharp corners, etc
- Look for derivative value, not the function value and questions about the ROC of
the function given in the table
T or F: Polynomials are always continuous and differentiable - ANSWERT
How to use MVT - ANSWER1. Check conditions
2. Find Aroc
3. Set number found for AROC to the deriative (IROC) and solve for x
Intermediate Value Theorem (IVT) - ANSWERIf f is continuous on the closed interval
[a,b] and k is any number between f(a) and f(b), then there is at least one number c
in [a,b] such that f(c)=k
What to look for for IVT - ANSWERIf its continous, the fuction value not the derative,
and questions about a function value not found in the table.
What could help us determine the interals where f(x) is increasing and decreasing -
ANSWERROC/derivative
Critical points/values - ANSWERA horizontal tangnet or corner/cusp
If f(x) is defined at x=c then f(x) has a crtical point at x = c if f'(c) = 0 or f'(c) is
undefniend
How to find a critical point given f(x) - ANSWER1. Find derative and set it equal to 0.
2. Create a sign chart to test
1st Derivative Test - ANSWERLet c be critical # of a function f that is cont. on open
interval I containing c. If f is differentiable on interval, except possibly at c⇒f(c) is
classified as:
1. If f'(x) changes from - to + at c, then f has rel. min at (c,f(c))
2. If f'(x) changes from + to - at c, then f has rel. max at (c,f(c))
