Important Questions - Monomath

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Calculus - Important Questions

1

IB HL Standard6 Marks

Find all local extrema of f(x) = x³ − 3x² − 9x + 5.

▶ Show Detailed Solution

f′(x) = 3(x−3)(x+1) = 0 ⇒ Critical points x = −1, x = 3.
f″(−1) = −12 < 0 ⇒ Local Max = 10 at x = −1.
f″(3) = 12 > 0 ⇒ Local Min = −22 at x = −22.