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5.3 Determining Intervals on Which a Function is Increasing or Decreasing

1 min readβ€’june 8, 2020

Sumi Vora

Sumi Vora


AP Calculus AB/BC ♾️

279Β resources
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πŸŽ₯Watch: AP Calculus AB/BC - Increasing and Decreasing Functions

Derivatives and Direction

The derivative of a function can tell us how the function looks when it is graphed. 😲
If the derivative is positive, then the function is increasing. βž• = ⬆️
If it is negative, then the function is decreasing.Β  βž– = ⬇️

Critical Values and Relative/Local Extrema

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 πŸ“Š
x
...
critical valueΒ 
...
etc.
f'(x)
+/-
0
+/-
etc.
πŸ’‘ Remember:
If the derivative is positive, then the function is increasing. βž• = ⬆️
If it is negative, then the function is decreasing.Β  βž– = ⬇️
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 
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πŸ‘‘Unit 1 – Limits & Continuity
πŸ€“Unit 2 – Fundamentals of Differentiation
πŸ€™πŸ½Unit 3 – Composite, Implicit, & Inverse Functions
πŸ‘€Unit 4 – Contextual Applications of Differentiation
✨Unit 5 – Analytical Applications of Differentiation
πŸ”₯Unit 6 – Integration & Accumulation of Change
πŸ’ŽUnit 7 – Differential Equations
🐢Unit 8 – Applications of Integration
πŸ¦–Unit 9 – Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)
β™ΎUnit 10 – Infinite Sequences & Series (BC Only)
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