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# AP Calculus Chapter

Question | Answer |
---|---|

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 |

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amandasiwek