Penjelasan dengan langkah-langkah:

A. f(x) = 2x³ + x² – 4x + 1

f'(x) = 3(2x³-¹) + 2(x²-¹) – 4

f'(x) = 6x² + 2x – 4

2(3x² + x – 2) = 0

2(3x –2)(x + 1) = 0

x1 = ⅔ , x2 = –1

jenis stasionernya x1 maksimum, x2 minimum

Nilai stasionernya :

f(⅔) = 2(⅔)³ + (⅔)² – 4(⅔) + 1

= 16/27 + 12/27 – 72/27 + 27/27

= (16+12+27–72)/27

= –17/27

Titik stasioner (⅔, –17/27)

f(–1) = 2(–1)³ + (–1)² –4(–1) + 1

= –2 + 1 + 4 + 1

= 4

Titik stasioner (–1, 4)

B. f(x) = x⁴ + 4x³ – 6

f'(x) = 4x³ + 12x²

4x²(x + 3) = 0

x1 = 0, x2 = –3

Nilai stasionernya :

f(0) = 0⁴ + 4(0)³ – 6 = –6

Titik stasioner (0, –6)

f(–3) = (–3)⁴ + 4(–3)³ – 6

= 81 – 108 – 6

= –33

Titik stasioner (–3, –33)