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AP Calculus Chapter

Absolute Maximum Value if and only if f(x)
Absolute Minimum Value if and only if f(x)>f(c)
The Extreme Value Theorem If f is continous on a closed interval, then f has both a maximum and minimum value on the interval
Local Maximum tallest point in local area
Local Minimum lowest point in the local area
If f1 exists at C then ______ f1(c)=0
A point in interior of the domain of a function f at which f1=0 or f1 does not exist is a ____ ______ of f. critical point
True or False: critical point are not always extremes true
Steps to finding maxs and mins 1. find the derivative and determine where it is zero and undefined. (CP) 2. find the value of the function at each critical point 3. Find slopes for points between the critical pts to determine max/min 4. check endpoints
a fraction does not exist when ______ equals zero. the denominator
If f(x) is continous at every pt of a closed interval and differentiable at every point then there is at least one point at which f1(c)=f(b)-f(a)/b-a Mean Value Thm
To solve for whether a function is increasing/decreasing you can set up what? Table. using inequalities
Antiderivative is the same as ______ taking the derivative backwards
The first derivative test it used to find local extrema but is also the same as _______. finding whether a function is increasing/decreasing.
The graph of f is above the tangent lines and f1 is increasing. concave up
means the graph of f is below the tangent lines and f1 is decreasing concave down
What are the 3 steps to determine concavity? 1. Locate x values at which f2=0 or undefined 2. use these x values to determine intervals 3. test the sign of f2 in each interval
A point where the graph of a functions has a tangent line and where the concavity changes point of inflection
Second Derivative Test Steps 1. Find Critical Points by setting f2(x)=0 2. Find f2(c) where c is a critical point 3. f2(c)>0 -local min f2(c)<0 -local max
For concavity you use the ______ derivative test second
for find extrema you use the _______ derivative test first
to find points of inflectiong you use the _____ derivative test. second
Max profit occurs when ________. the derivative of revenue equals the derivative of cost r1(c)=c1(c)
the production level at which average cost is smallest is a level at which the __________. average cost equals the marginal cost
Means to create a linera equation approximating the curve linearization
y-y1=m(x-x1) point slope formula
Differential means derivative
Estimate of Change ds=f1(a)dx
4/3πr^3 volume of sphere
1/3πr^2h volume of cone
4πr^2 surface area of sphere
lwh volume of rectangular box
2lw+2lh+2wh surface area of rectangular box
a^2+b^2=c^2 pythagorean thm
1/2bhl volume of triangular prism
SOH CAH TOA is only used for ______/ right triangles
2πr circumference of circle
πr^2 area of circle
6s^2 surface area of a cube
x^2+y^2=r^2 equation of a circle
x^2+y^2=1 unit circle
Created by: amandasiwek