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5.3 Determining Intervals on Which a Function is Increasing or Decreasing

Sumi Vora

AP Calculus AB/BCΒ βΎοΈ

279Β resources
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π₯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.Β π²
If the derivative is positive, then the function is increasing. β = β¬οΈ
If it is negative, then the function is decreasing.Β  β = β¬οΈ

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 π
 x ... critical valueΒ ... etc. f'(x) +/- 0 +/- etc.
π‘ Remember:
If the derivative is positive, then the function is increasing. β = β¬οΈ
If it is negative, then the function is decreasing.Β  β = β¬οΈ
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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