AP CALCULUS BC CHAPTER 4 |
COMPLETE STUDY GUIDE, PRACTICE
QUESTIONS, FORMULAS & EXAM
REVIEW 2026 | GRADED A+ |
GUARANTEED SUCCESS
Updated 2026 Questions and Answers | 100% Verified
Exam Prep and Comprehensive Rationales Included
, Absolute Min Value if and only is f(x) is greater than or equal to f(c) for all x in Domain
Extreme Value Theorem if f=continuous on closed interval [a,b] then f has both a max and min value on the
interval
Critical Point Point in the domain where f' (f prime=derivative of function f)= 0 or does not exist
(DNE). Not always the max and min
Local Extreme Value=Relative extremes Local Max= max value in open interval
Local Min=min value in open interval
Horizontal tangents occur: when dy/dx (derivative) is equal to 0
Steps to find Extreme Values: 1- Find derivative, set it = 0.
2-Plug in x in original to find y value
3-Find values or slopes between critical points to find max/min values- use
number line?
4- for closed intervals, check endpoints
Mean Value Theorem if f(x) is continuous over [a,b], and differentiable over (a,b), then, at some point c
between a and b:
f ' (c)= f(b)-f(a)/b-a = y-y/x-x= slope
- positive value= increase, negative value= decrease
First Derivative rules y'=positive=rising curve, above x axis
y'=negative= falling curve= below x axis
y'=0, possible local max or min
Second derivative rules y''= positive= concave up (up like a cup, smiley face)
y''=negative= concave down (down like a frown, sad face)
y''=0, possible inflection point where concavity changes (up become down, vice
versa)
*derivative test is making a number line and finding positive or negative at
derivative values
setting second derivative equal to zero will find the inflection points
Optimization Maximizing or minimizing an aspect of something
Reminder way to find max or min value of function 1- write in terms of one variable
2-set first derivative = 0
3- check endpoints if necessary
Other notes/rules: - if more then one variable, consolidate it to one using substitution
-check if endpoints/ extremes are max or min value
COMPLETE STUDY GUIDE, PRACTICE
QUESTIONS, FORMULAS & EXAM
REVIEW 2026 | GRADED A+ |
GUARANTEED SUCCESS
Updated 2026 Questions and Answers | 100% Verified
Exam Prep and Comprehensive Rationales Included
, Absolute Min Value if and only is f(x) is greater than or equal to f(c) for all x in Domain
Extreme Value Theorem if f=continuous on closed interval [a,b] then f has both a max and min value on the
interval
Critical Point Point in the domain where f' (f prime=derivative of function f)= 0 or does not exist
(DNE). Not always the max and min
Local Extreme Value=Relative extremes Local Max= max value in open interval
Local Min=min value in open interval
Horizontal tangents occur: when dy/dx (derivative) is equal to 0
Steps to find Extreme Values: 1- Find derivative, set it = 0.
2-Plug in x in original to find y value
3-Find values or slopes between critical points to find max/min values- use
number line?
4- for closed intervals, check endpoints
Mean Value Theorem if f(x) is continuous over [a,b], and differentiable over (a,b), then, at some point c
between a and b:
f ' (c)= f(b)-f(a)/b-a = y-y/x-x= slope
- positive value= increase, negative value= decrease
First Derivative rules y'=positive=rising curve, above x axis
y'=negative= falling curve= below x axis
y'=0, possible local max or min
Second derivative rules y''= positive= concave up (up like a cup, smiley face)
y''=negative= concave down (down like a frown, sad face)
y''=0, possible inflection point where concavity changes (up become down, vice
versa)
*derivative test is making a number line and finding positive or negative at
derivative values
setting second derivative equal to zero will find the inflection points
Optimization Maximizing or minimizing an aspect of something
Reminder way to find max or min value of function 1- write in terms of one variable
2-set first derivative = 0
3- check endpoints if necessary
Other notes/rules: - if more then one variable, consolidate it to one using substitution
-check if endpoints/ extremes are max or min value
