1 min readβ’june 8, 2020

Sumi Vora

π₯**Watch: AP Calculus AB/BC - ****Increasing and Decreasing Functions**

The derivative of a function can tell us how the function looks when it is graphed.Β π²

The x-values when the derivative is 0 are called **critical values**. Critical values can also occur when f'(x) does not exist or at the endpoints of the domain of f'(x). Critical values are most important in determining where a function reaches a **relative extreme **value. (these are also called **local extreme **values)Β

To find the critical points on a graph, find f'(x) and set it equal to 0 to find x. Next, determine whether they are a relative minimum, relative maximum, or neither by making a *sign chart*:Β π

x | ... | critical valueΒ | ... | etc. |

f'(x) | +/- | 0 | +/- | etc. |

If the sign of f'(x) changes from positive to negative (increasing to decreasing), then it is a **relative maximum**. If it changes from negative to positive (decreasing to increasing), it is a **relative minimum**.Β

Browse Study Guides By Unit

πUnit 1 β Limits & Continuity

π€Unit 2 β Fundamentals of Differentiation

π€π½Unit 3 β Composite, Implicit, & Inverse Functions

πUnit 4 β Contextual Applications of Differentiation

β¨Unit 5 β Analytical Applications of Differentiation

π₯Unit 6 β Integration & Accumulation of Change

πUnit 7 β Differential Equations

πΆUnit 8 β Applications of Integration

π¦Unit 9 β Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)

βΎUnit 10 β Infinite Sequences & Series (BC Only)

π§Multiple Choice Questions (MCQ)

βοΈFree Response Questions (FRQ)

πBig Reviews: Finals & Exam Prep

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