aplikasi turunan, deret geometri

f(x) = -2x³ + 6x + 6x + 1

syarat maks/min → f'(x) = 0

f'(x) = 0

-6x² + 6 = 0

x² - 1 = 0

x = 1 atau x = -1

interval -1 ≤ x ≤ 2

f(-1) = -2(-1)³ + 6(-1) + 1 = -3

f(1) = -2.1³ + 6.1 + 1 = 5

f(2) = -2.2³ + 6.2 + 1 = -3

nilai minimum = -3

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deret geo tak hingga

U2 - U1 = f'(0) = -6.0² + 6 = 6

ar - a = 6

a(r - 1) = 6

a = 6/(r - 1)

S∞ = -3

a/(1 - r) = -3

6/(r - 1)(1 - r) = -3

-6/(r - 1)² = -3

(r - 1)² = 2

r - 1 = ± √2

r = 1 ± √2

rasio yg mungkin :

r = 1 - √2 atau r = 1 + √2