AP Calculus AB / Unit 5: Analytical Applications of Differentiation
5.3 Determining Intervals on Which a Function Is Increasing or Decreasing
Notes
- $f'>0$ on an interval means $f$ is increasing; $f'<0$ means decreasing.
- Find critical points, then test the sign of $f'$ in each interval between them.
Practice
$f'(x)=(x-1)(x+3)$. On which interval is $f$ decreasing?
$f'<0$ between the roots.
$f(x)=e^{-x}$ is:
$f'=-e^{-x}<0$.
Justifying "$f$ is increasing on $(2,5)$" requires:
The sign of the first derivative decides.
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