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Calculus · DER

Increasing and Decreasing Intervals Using the First Derivative

f is increasing where f'(x) > 0 and decreasing where f'(x) < 0. Critical points are where f'(x) = 0 or undefined.

CalculusCommon Core FUN-1.ADERVerified correct ✓

Worked examples

Let f(x) = x³ - 27x. Find all critical numbers by setting f'(x) = 0. Enter the smallest critical number.
Answer: -3
Let f(x) = x² - 4x + 5. Find all critical numbers by setting f'(x) = 0. Enter the critical number.
Answer: 2

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