AP Calculus AB / Unit 5: Analytical Applications of Differentiation

5.4 Using the First Derivative Test to Determine Relative (Local) Extrema

3 practice questions

Notes

At a critical point $c$:

$f'$ changes from $+$ to $-$: local max.
$f'$ changes from $-$ to $+$: local min.
No sign change: neither.

Practice

$f'(x)=x^2(x-2)$. At $x=0$, $f$ has:

Using the same $f'$, at $x=2$, $f$ has:

$f'$ changes from positive to negative at $x=4$. Then:

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